Defining the word teleios before looking at the passages in which it is used is very helpful to gather understanding.  But always remember the context of a passage brings out the proper shade of meaning.  I pray the following is helpful in laying a groundwork of our study of teleios

The Complete WordStudy Dictionary gives the following definition: Finished, that which has reached its end, term, limit; hence, complete, full, wanting in nothing.  Téleios can be used in a relative or absolute sense as in Matthew 5:48 and Matthew 19:21.  God’s perfection is absolute; man’s is relative.  The téleios is one who has attained moral maturity, the goal for which he was intended, namely, to be a man obedient in Christ. 

Thayer’s Greek Definitions offers the following: 1) brought to its end, finished; 2) wanting nothing necessary to completeness; 3) perfect; 4) that which is perfect; 4a) consummate human integrity and virtue 4b) of men; 4b1) full grown, adult, of full age, mature.

Henry Alford’s Greek New Testament in its treatment of teleios in Matthew 5:48 adds: complete, in your love of others; not one-sided, or exclusive, as these just mentioned, but all-embracing, and God-like.  No countenance is given by this verse to the ancient Pelagian or the modern heresy of perfectibility in this life.  Such a sense of the words would be utterly at variance with the whole of the discourse.  See especially Matthew 5:22, 29, and 32, in which the imperfections and conflicts of the Christian are fully recognized.  Nor, if we consider this verse as a solemn conclusion of the second part of the Sermon, does it any the more admit of this view, asserting as it does that likeness to God in inwardpurity, love, and holiness, must be the continual aim and end of the Christian in all the departments of his moral life.  But how far from having attained this likeness we are, St. Paul shows us in Philippians 3:12; and every Christian feels, just in the proportion in which he has striven after it.  (Emphasis in the original)

In Studies in the Vocabulary of the Greek New Testament Kenneth Wuest says the following,

Telaios the adjective, and teleioo the verb.  The adjective is used in the papyri, of heirs being of age, of women who have attained maturity, of full-grown cocks, of acacia trees in good condition, of a complete lampstand, of something in good working order or condition.  To summarize; the meaning of the adjective includes the ideas of full-growth, maturity, workability, soundness, and completeness.  The verb refers to the act of bringing the person or thing to any one of the aforementioned conditions.  When applied to a Christian, the word refers to one that is spiritually mature, complete, well-rounded in his Christian character.  

Therefore, as for you, you shall be those who are complete in your character, even as your Father in heaven is complete in His being.  (Wuest’s Expanded Translation)

As The Plow desires to present the Scripture as a means of transforming the character of the disciple, teleios is the life of maturity the disciple sets as his goal, the goal of Christ-like character.  The disciple lives as he was intended to live when teleios is the end game.