First, understand that various different denominations may have different views on the subject. I'm going to answer from a conservative evangelical perspective.
The Bible doesn't give a reason or a purpose for marriage other than the fact that it's something that was established by God in the Garden of Eden. (Whether you take the Genesis account literally or allegorically, the first recorded marriage is there.)
Before everyone points out that there's no wedding ceremony of mention of Adam and Eve being married, let's look at a few verses: (Emphasis mine)
From Genesis 2: (KJV)
8 And the Lord God said, It is not good that the man should be alone;
I will make him an help meet for him.
19 And out of the ground the Lord God formed every beast of the field,
and every fowl of the air; and brought them unto Adam to see what he
would call them: and whatsoever Adam called every living creature,
that was the name thereof.
20 And Adam gave names to all cattle, and to the fowl of the air, and
to every beast of the field; but for Adam there was not found an help
meet for him.
21 And the Lord God caused a deep sleep to fall upon Adam, and he
slept: and he took one of his ribs, and closed up the flesh instead
22 And the rib, which the Lord God had taken from man, made he a
woman, and brought her unto the man.
23 And Adam said, This is now bone of my bones, and flesh of my flesh:
she shall be called Woman, because she was taken out of Man.
24 Therefore shall a man leave his father and his mother, and shall
cleave unto his wife: and they shall be one flesh.
25 And they were both naked, the man and his wife, and were not
I've been to many weddings,from many traditions, and these verses are read at almost all of them. Catholic, Baptist, Methodist, Lutheran, across the board, these verses are used in the wedding ceremony, and the Priest, preacher, pastor usually refers to those as the first marriage, and used a phrase like "Marriage was ordained by God.
So, one Biblical reason for marriage is that it was ordained by God, and therefore, as obedient children of God, we should want to do as He has ordained.
However, Paul, in 1 Corinthians gives another, practical reason: To avoid fornication. In layman's terms, he's saying that he wishes that all men could be like him and abstain, but since most of us can't abstain, it's better to keep your sexual practices within the bounds of marriage:
1 Corinthians 7
King James Version (KJV)
7 Now concerning the things whereof ye wrote unto me: It is good for a
man not to touch a woman.
2 Nevertheless, to avoid fornication, let every man have his own wife,
and let every woman have her own husband.
3 Let the husband render unto the wife due benevolence: and likewise
also the wife unto the husband.
4 The wife hath not power of her own body, but the husband: and
likewise also the husband hath not power of his own body, but the
5 Defraud ye not one the other, except it be with consent for a time,
that ye may give yourselves to fasting and prayer; and come together
again, that Satan tempt you not for your incontinency.
6 But I speak this by permission, and not of commandment.
7 For I would that all men were even as I myself. But every man hath
his proper gift of God, one after this manner, and another after that.
8 I say therefore to the unmarried and widows, it is good for them if
they abide even as I.
9 But if they cannot contain, let them marry: for it is better to
marry than to burn.
I think the first half is a better answer - We participate in marriage because we believe that God ordained it, but I can't discount the teaching from Corinthians, so I included it.
Other than those two, there are no direct Biblical reasons for marriage. At least not in the sense that "The Bible says you should get married because..." There are verses within Scripture that speak about how marriage is good, marriage is beneficial, a good wife is to be treasured, etc, but all of those would be outside the scope of the question, as would speculation about why God wants what God wants.
What your friend said may or may not be true. Since the Biblical answer given above has nothing to do with furthering the kingdom of heaven, I'd question her choice of word in saying that the idea that a married couple can do more is the only reason to get married. There are clearly other reasons.
I might not disagree of she'd said "The only reason I would want to get married" instead of "The only reason to get married".