What message did Jesus Christ tried to give by comparing the Kingdom Of God(Isn't that Heaven?) with the mustard seed and yeast?
Here Jesus teaches that He has come to prepare us for the kingdom of heaven (Matt. 13.31) and this kingdom of heaven has to be first created within us if we have to be partners of that kingdom. This kingdom is created within us by His message of Gospel which is simplest of all.
The Gospel message has immense potential to change the medium where it is taught: be it a person, or region or the world. That is what it has done to the world in spite of people severely prosecuting at the onset, the simpleton disciples of Jesus.
The quantity of yeast is minuscule compared to the whole dough, yet it makes full dough to rise with its unique effect. The size of a mustard seed is negligible compared to all other seeds yet it grows into a large plant.
So is the message of Gospel compared to works of other great thinkers and philosophers. It is in simple words and parables yet it is a goldmine full of wisdom and is understandable even to unlearned and lowly. It has the power to change the face of the world and it did. It has the power to win the wisest and make their wisdom appear to be foolish.
Jesus was saying that the Kingdom of God has a huge effect on whatever it interacts with. That is, the effect is disproportionately large in comparison to what we mortals perceive the Kingdom of God to be.
The Kingdom of God refers to more than just Heaven. The Kingdom of God also includes his people, many of whom are still here on Earth.
There are already two good answers here representing the typical interpretation of these parables, that the rapid growth of the mustard plant and yeast are pictures of the rapid growth of Christianity, so I'd like to offer a contrasting view: these parables are actually a warning about corruption within the Church.
This is a minority view (see sources below), and I realize that people much more gifted than I am have drawn out some wonderful lessons based on the standard interpretation, but I think the context and language of that passage of scripture actually point in another direction, while still being consistent with Jesus' other teachings about the Kingdom.
Context: these parables occur together in both Matthew 13 and Luke 13
Language: if we assume that certain symbols are used consistently throughout the Bible, a different picture starts to emerge.
As other answers have already said Jesus taught that the Kingdom of God / Kingdom of Heaven (basically synonyms) is more than just Heaven (in the sense of an afterlife); it is a kingdom composed of everyone who submits to God's rule in their hearts -- in a word, the Church. However, when we look at Christ's followers across history (from a human perspective) we don't see a single unified kingdom -- we see a mess: "political intrigue, lust for power, intolerance, vain superstition, immorality, and greed" -- in other words, false religion.
We should take comfort therefore, that Jesus warned us from the beginning that His Kingdom would be intermingled with the influence of its enemies. And (if you will forgive a little preaching in this Q&A format), we should also put this into perspective by remembering that each of us is susceptible to hypocrisy, sin, and holding false ideas about God. If I want His Kingdom to spread on earth, I need to start by examining how fully that Kingdom really rules in my own life.
Full disclosure: while researching this answer, I've found that this interpretation seems to be typical only among (Dispensational?) Premilennialist teaching.
The Kingdom of God is NOT EXACTLY a place in every parable that has this line. It is the reign or kingship of God, God who rules, rather than a place where God rules.
The Parable of the Mustard Seed signifies the kingdom/reign of God's sudden and surprising transformation from its almost invisible beginning to its full grandeur. It's described to be dynamic or active.
The Parable of the Yeast explains that like the yeast, the reign of God transforms human history by infusing into its activity the invisible spirit of and power of God. The Universal expansion of the reign of God expects not necessarily an acceptance by all but a universal disturbance created in the world by those who do accept. This is a disturbance like that of the leaven that cause the dough to rise. The KOG is the yeast, God is the baker, and we (man) are the dough. It is described as transformative because it allows us to change for the better, so we should do good things from the heart.
I read it from my school textbook by the way.
Parable of yeast is to me a metaphor for the work of the Father, Son and Spirit (the 3 balls of dough) and the workings and transformation within a believers life over time allocated.The yeast cannot be seen to work but its manifestations are dramatic, growing over time and undoubted.. as is regeneration. The Mustard seed parable to me is the bigger picture of Our Lords Ministry and for the workings of Our Lord within a world view, the yeast more personal.
The parables of the mustard seed and of yeast are short but enigmatic. It seems that parables so mysterious must have a deep underlying meaning, and so they have been the subject of much speculation over the centuries.
The earliest New Testament reference to the parable of the mustard seed is found in Mark, at verses 4:30-32, as one of a series of parables that did not include the parable of yeast. Mark is comparing the rule of God to "greatest of plants" which grows from this tiny mustard seed:
The parable of the mustard seed is also considered to have occurred in the hypothetical 'Q' document, where it is followed by the parable of yeast. It is this version of the parable that we see in Matthew and Luke, shown here with the parable of yeast:
Middle eastern mustard (s. hirta) does not grow into great trees, but is for farmers a noxious weed. Mark's version (with a similar version found in the non-canonical Gospel of Thomas) of the parable of the mustard seed recognises this, comparing the mustard seed as the smallest of seeds that grows to a large "herb" (laxanon). It does not call it a "great tree" and only has birds rest under the shadow of it, not in its great branches. The emphasis upon the contrast of the small seed and the large plant is missing in the Q form (Matthew, Luke) of this parable, in spite of saying that it becomes a 'tree' (dendron) and that the birds are nesting in its branches.
Mark's version thus has the clearest meaning and most realistic simile when it compares the rule of God to mustard, in that it can grow from the smallest seed. The 'Q' version (Matthew, Luke) appears to have attempted to echo references from the Books of Ezekiel and Daniel, about a tiny sprig growing to become a giant "noble cedar” with roots that spread across the earth, branches reaching to heaven, fruit for all, and shelter for animals and birds, but in doing so reads almost like a parody.
Rex Wyler, in The Jesus Sayings, page 111, believes the parable of the leaven in the flour, in the following verses (Matthew 13:33; Luke 13:20-21), appears simply to satirise a story (Genesis 18:6) about Sarah, who used three measures of choice flour to bake cakes for heavenly messengers visiting Abraham.
Very simply put, the kingdom of God is the kingdom of faith which is both present and coming. This can be understood as the church which is the kingdom of faith. Mustard seed is used only five times in the Bible.
Mat_13:31 Another parable put he forth unto them, saying, The kingdom of heaven is like to a grain of mustard seed, which a man took, and sowed in his field:
Mat_17:20 And Jesus said unto them, Because of your unbelief: for verily I say unto you, If ye have faith as a grain of mustard seed, ye shall say unto this mountain, Remove hence to yonder place; and it shall remove; and nothing shall be impossible unto you.
Mark 4:31, Luke 13:19, 17:6
Rom_14:17 For the kingdom of God is not meat and drink; but righteousness, and peace, and joy in the Holy Ghost.