Ok, so you've boned up on your overused chord progressions and you've been learning your scale degrees and other diatonic information which is important to your compositions. You should also know what chords are built off of said scale degrees, for example in the key of C major:
I is Cmaj7
ii is Dmi7
iii is Emi7
IV is Fmaj7
V is G7 (G dominant 7)
vi is Ami7
vii is B half-diminished or Bmi7b5
Great! And we also know that a I chord, Cmaj7 in our case, can go to pretty much whatever it wants to, and that strong progressions like to go to the dominant V or vii chords, because they propel back to the I, giving a nice resolution to the piece. For example, a pretty standard diatonic progression would be something like
I iii vi ii V i or Cmaj7, Emi7, Ami7, Dmi7, G7, Cmaj7. Fan-tastic!
Try it out if possible, you'll hear where the progression "wants" to go before the next chord is played, thanks to scale drives and good ol' fashioned voice leading. Now, let's see we get bored with said standard progression. We want to use some other chords, with different flavors...but we don't just want to extend the chords into other registers (yielding things like Dmi9 or Cmaj11), we want to take some chords that are a bit further out of our normal scope, we want to bid our friend the key of C major adieu, at least momentarily, and modulate to another key. Now, how do we do this? There's several ways, but only a few of which are "right" and even less which actually sound good. We could just go from that last I chord in our progression to a new I chord, let's say in G...but we've already established that the G chord in this key is a dominant 7, not a major 7...we will sound like we've made a mistake and/or are lost in our own work...although we will be, technically, in the key of G major. Now, perhaps we'd like to be a bit more slick about things and actually modulate, as the term suggests, into the new key. Well, we know that the V and the vi chords, because of their tonality and scale drive "want" to resolve to the I chord of their respective keys. So, what we should do is "borrow" some of these dominant chords from the key we want to modulate to, G major.(remember, harmony is analyzed by function).
So from our last I chord, Cmaj7, let's say we go again to that Emi7 (iii chord) and then on to our Ami7 (the vi chord), but then we jump to the ROOT of our ii chord (Dmi7), D but instead of a minor 7 we play a D7, which is the dominant V chord to G major. Now, yes we sound out of key, but we used our Ami7 (vi chord) to ACT as a minor ii chord in G major, leading us quite strongly to the D7. The D chord, since it's no longer a minor 7, but a dominant 7 is analyzed no more as our ii, but as our V7 of V or V7/V, which means that it is the dominant V chord of G major, and G is the V of our original key. Got all that? So, now that we've established the new key with our brand spankin' new D7 chord that we borrowed from G major, we can easily resolve that to the Gmaj7 chord. This little idea is commonly referred to as "ii V'ing" since that's what we did, making the vi of C maj act as the ii of G maj, and then changing the Dmi7 ii chord into the D7 V chord, giving us our new ii V progression, leading to one. A ii V I is pretty stock in most jazz standards, and although it is used widely and somewhat dryly at times, it's also used creatively to propel a tune into different places/keys, and in much more bizarre ways than this...but more on that later. If one so desired, they could probably ii V I their way into Hell, and possibly back...though I wouldn't recommend it. Have fun! :)