Matthew 7:15-20
15 Beware of false prophets, which come to you in sheep's clothing, but inwardly they are ravening wolves.
16 Ye shall know them by their fruits. Do men gather grapes of thorns, or figs of thistles?
17 Even so every good tree bringeth forth good fruit; but a corrupt tree bringeth forth evil fruit.
18 A good tree cannot bring forth evil fruit, neither can a corrupt tree bring forth good fruit.
19 Every tree that bringeth not forth good fruit is hewn down, and cast into the fire.
20 Wherefore by their fruits ye shall know them.
Luke 6:43-45
43 For a good tree bringeth not forth corrupt fruit; neither doth a corrupt tree bring forth good fruit.
44 For every tree is known by his own fruit. For of thorns men do not gather figs, nor of a bramble bush gather they grapes.
45 A good man out of the good treasure of his heart bringeth forth that which is good; and an evil man out of the evil treasure of his heart bringeth forth that which is evil: for of the abundance of the heart his mouth speaketh.
These two parallel passages from the Sermon on the Mount are occasionally used to teach that unless a Christian obeys God to some undefined degree, then they will go to Hell, often with the emphasis on Matthew 7:19 in particular.
Note how closely Matthew 7:19 mirrors what John the Baptist preached in Matthew 3:10 and Luke 3:9. These passages are covered in this article, which is a good primer to what's being discussed here as well.
Matthew 7:15 gives us the purpose statement of what's being said - a warning to "beware of false prophets, which come to you in sheep's clothing, but inwardly they are ravening wolves". Since they "come in sheep's clothing", we are to discern them as wolves by their "fruits" (Matthew 7:16-20, Luke 6:43-45).
The "fruit" being spoken of here is doctrine, as we can learn by taking a look at another very similar statement of Christ:
Matthew 12:33-35
33 Either make the tree good, and his fruit good; or else make the tree corrupt, and his fruit corrupt: for the tree is known by his fruit.
34 O generation of vipers, how can ye, being evil, speak good things? for out of the abundance of the heart the mouth speaketh.
35 A good man out of the good treasure of the heart bringeth forth good things: and an evil man out of the evil treasure bringeth forth evil things.
The false prophets outwardly appear (works, lifestyle, tone, etc.) like a Christian - that's the "sheep's clothing". However, once they open their mouths, they are discerned as wolves by their corrupt doctrine.
Therefore, we can see their "fruit", and discern what kind of "tree" they are, because "a tree is known by his fruit", and "a good tree bringeth not forth corrupt fruit; neither doth a corrupt tree bring forth good fruit".
Since Christ is using a similitude - likening human beings to trees, in this case - He uses hyperbole. He is speaking of the fact that, as a general rule, saved preachers will preach the truth, and unsaved ones won't. He is not saying that Roman Catholic priests aren't occasionally right about the virgin birth, or the deity of Christ, or that a saved pastor only teaches 100% correctly on every doctrine. We can use our God-given common sense to recognize when Christ uses hyperbole.
So, the primary application of these passages has nothing to do with some commandment to look at other Christians' lifestyles to see if they are "truly saved", as these passages are often used to teach. They have to do with examining the doctrine of preachers.
They can, however, be used to teach on a general truth about abiding in Christ that applies to Christians also, beyond their primary context in regard to false prophets, which is covered in the aforementioned article on Matthew 3:10 and Luke 3:9.
These passages teach that the way someone lives is sparse indication of whether or not they are a "good tree". A blatantly sinful false prophet would be seen a mile away, because they would be a wolf wearing wolves' clothing.
Instead, Christ implores us to train ourselves to detect false doctrine, as a false prophet's teaching and words are what will betray them as what they truly are inside.