In standard knitting most of the time you form the knit stitch by putting your needle through the front loop on the needle. The exception to this rule is combination knitting, which is worked in such a way that the purl stitches are twisted, so the knit stitches must be worked through the back loops in order for the knitting to come out looking like the nice flat Vs to which we are all accustomed.
To knit through the back loop, you form the stitch in exactly the same way, but on the loop at the back of the needle instead of the loop at the front of the needle. It is, of course, the same loop regardless of where you go through it, and you enter it in the same way, from the front of the work to the back, you just go into the back part of the stitch instead of the front.
Knitting through the back loop (indicated in knitting patterns as k tbl, knit in the back of the stitch, k1-b) is also an easy way to twist a knitting stitch, which gives a different texture to the surface of your knitting. If you work a lot of twisted stitches, such as the Twisted Stockinette Stitch where every stitch of every row is twisted, you get a much firmer fabric than you would working regular Stockinette.
Some stitch patterns that use twisted stitches do not use as many of them, so the fabric is more like what you'd expect from knitting. Rice Stitch is one example. Because only half the stitches are twisted on every other row, the fabric stays less dense than it would be if more stitches were twisted. Knit through the back loop is a lot more common than its counterpart purl through the back loop, but it's handy to know how to do both in case you ever need them.
There's another reason you might knit through the back loop that has nothing to do with the stitch pattern you're working and everything to do with recovering from a bad knitting situation. Sometimes your stitches will fall off the needle, or you'll have taken stitches off the needle to frog, or you'll need to fix a dropped stitch. When any of these things happen, there's a potential for putting the stitches back on the needle incorrectly, because you're just in a hurry to keep the stitches from falling further or because you don't know how to look at a stitch and mount it on the needle correctly.
If you have your stitches twisted on the needle and you knit through what is on the front of your needle but is actually the back loop, you'll end up with twisted stitches. If you notice the stitches are twisted on the needle—one clue is that they're harder to knit through than usual, if visual inspection doesn't help you—you could physically untwist them, or you could knit through the back loop, which is actually the front loop, just at the back of the needle, which untwists the stitch.