Arthur Pink gives an outstanding explanation of total depravity in his book The Total Depravity of Man. You can download a free e-book of this excellent work on the link given. Here are a few excerpts:

It is a sadly neglected subject. Notwithstanding the clear and uniform teaching of Scripture, man’s ruined condition and alienation from God are but feebly apprehended and seldom heard in the modern pulpit, and are given little place even in what are regarded as the centers of orthodoxy. Rather the whole trend of present-day thought and teaching is in the opposite direction, and even where the Darwinian hypothesis has not been accepted, its pernicious influences are often seen. In consequence of the guilty silence of the modern pulpit, a generation of churchgoers has arisen which is deplorably ignorant of the basic truths of the Bible, so that perhaps not more than one in a thousand has even a mental knowledge of the chains of hardness and unbelief which bind the natural heart, or of the dungeon of darkness in which they lie. Thousands of preachers, instead of faithfully telling their hearers of their woeful state by nature, are wasting their time by relating the latest news of the Kremlin or of the development of nuclear weapons.

It is therefore a testing doctrine, especially of the preacher’s soundness in the faith. A man’s orthodoxy on this subject determines his viewpoint of many other doctrines of great importance. If his belief here is a scriptural one, then he will clearly perceive how impossible it is for men to improve themselves—that Christ is their only hope. He will know that unless the sinner is born again there can be no entrance for him into the kingdom of God. Nor will he entertain the idea of the fallen creature’s free will to attain goodness. He will be preserved from many errors. Andrew Fuller stated, “I never knew a person verge toward the Arminian, the Arian, the Socinian, the Antinomian schemes, without first entertaining diminutive notions of human depravity or blameworthiness.” Said the well-equipped theological instructor, J. M. Stifler, “It cannot be said too often that a false theology finds its source in inadequate views of depravity.”

Read more here.