Therefore you shall be perfect, just as your Father in heaven is perfect. (Matthew 5:48 NKJV)
So, God expects us to be perfect. What is meant by "perfect"? How can any human be without error, this side of heaven?
In Koine Greek, Matthew 5:48 reads as follows:
ἔσεσθε οὖν ὑμεῖς τέλειοι ὡς ὁ πατὴρ ὑμῶν ὁ οὐράνιος τέλειός ἐστιν.
The key word here is telos, which is often translated as 'perfect' but can equally well be translated "goal, end, or purpose." The telos of a thing is that point to which a thing yearns to be, the purpose for which a thing was built.
It does not imply that perfection has been attained, but it is the trajectory towards which the essence of a thing strives.
In the case of "Be ye perfect," it is completely legitimate to translate telos in the sense of "Be that which God has designed you to be." As Jude 24 implies, we are being made fit to stand in the presence of God - it is the end for which we are made. Jesus is exhorting us here to be that which God would have eventually be, but he is not necessarily demanding we are already there.
These are the places in which telos is used. The ESV likes to use the word 'mature' to capture this sense.
1 Cor 14:20 NA27 w/GRAMCORD μὴ παιδία γίνεσθε ταῖς φρεσὶν ἀλλὰ τῇ κακίᾳ νηπιάζετε, ταῖς δὲ φρεσὶν τέλειοι γίνεσθε. 20 Brothers, do not be children in your thinking. Be infants in evil, but in your thinking be mature.
Here, the tie with our behavior is explicit, contrasting the maturity of our walk with the innocence of our understanding in regards to evil.
Phil 3:15 NA27 w/GRAMCORD Ὅσοι οὖν τέλειοι, τοῦτο φρονῶμεν· καὶ εἴ τι ἑτέρως φρονεῖτε, καὶ τοῦτο ὁ θεὸς ὑμῖν ἀποκαλύψει· Let those of us who are mature think this way, and if in anything you think otherwise, sGod will reveal that also to you
Here, maturity conveys the sense of growth - the way in which we will grow.
Col 4:12 NA27 w/GRAMCORD Ἰησοῦ], πάντοτε ἀγωνιζόμενος ὑπὲρ ὑμῶν ἐν ταῖς προσευχαῖς, ἵνα σταθῆτε τέλειοι καὶ πεπληροφορημένοι ἐν παντὶ θελήματι τοῦ θεοῦ. ...that you may stand mature and fully assured in all the will of God
Again, like Jude, the sense of maturity, steadfastness, and being what God designed you to be.
James 1:4 NA27 w/GRAMCORD ἡ δὲ ὑπομονὴ ἔργον τέλειον ἐχέτω, ἵνα ἦτε τέλειοι καὶ ὁλόκληροι ἐν μηδενὶ λειπόμενοι. Count it all joy, my brothers, when you meet trials of various kinds, for you know that the testing of your faith produces steadfastness. And let steadfastness have its full effect, that you may be perfect and complete, lacking in nothing.
Here, the fullness of the text probably does the best job of conveying that perfection is a process, begun by suffering, strengthened into steadfastness, and made complete in the perfection - the end state towards which all of this is pointing.
This question might be more suitable for Hermeneutics. But, at the same time it has some important theological value.
There is a wiki page for this verse alone.
I am not expert in hermeneutics but I believe that this verse is equivalent to this verse.
1 Peter 1:16 (NIV) for it is written: “Be holy, because I am holy.”
One of the most important mission of Jesus while He was on earth was to make us realize that we cannot meet the standard of God in our pursuit of holiness and perfection. Jesus pointed out that violating even one law means to violate the whole commandments. Even the sinful things we contemplate in our hearts without actually doing it is equivalent to committing it in real.
Jesus wanted to make us understand that we cannot meet the standard of God and that we need Jesus himself to set things right by pouring out His blood as a perpetual sacrifice to God. We do not need to achieve perfection but we need forgiveness.
Therefore, we need Jesus Christ in order to be counted as perfect in the eyes of God.
Hebrews 5:8-9 (NIV) Son though he was, he learned obedience from what he suffered and, once made perfect, he became the source of eternal salvation for all who obey him
Hebrews 10:10 (NIV) And by that will, we have been made holy through the sacrifice of the body of Jesus Christ once for all.
The world's definition of being perfect means that you don't make any mistakes or that you think that you are better than others. GOD'S definition of perfect according to the bible means that you are mature in the word of GOD, that you are mature in love, and are able to bridle(keep your mouth from guile) your tongue, in the book of James says than you are a perfect person! Also being attentive to the widows and the orphans in their tines of distress is pure, true and perfect undefiled religion in the sight of GOD!