English and Continental (or European) knitting are the two major styles of knitting, from which each knitter takes their own personal style. The difference has to do with the way a stitch is made – by 'throwing' in English-style knitting, or 'picking' in Continental-style, and each produces slightly different results and suits different sorts of knitters. The one you choose for each project is completely up to you; neither is 'better' than the other, but they are different enough that it's worth understanding both and knowing how each could benefit your knitting.
The defining difference between English vs. Continental knitting is all in the way the next bit of yarn is picked up in order to make a stitch. In English knitting, the yarn is 'thrown' around the needle – wrapped with the index finger of the right hand around the right needle after the stitch has been partially slipped from left to right. In Continental knitting, the yarn is 'picked' onto the right-hand needle from where it is held out in front of the left-hand needle. Continental knitting is often considered by seasoned knitters to be faster and easier on the hands, since they don't need to be held as awkwardly, but English knitting produces a smaller, more even stitch. If you have difficulty with the more commonly taught English-style as a left-handed knitter, it might be worth your while looking in to Continental knitting, since the left hand does most of the work.
Continental knitting is especially useful for garments that are intended to be closely fitted, since each stitch has a little more give to it, giving the whole piece a greater capacity for stretching and allowing it to be knitted a little smaller so that it will conform to the shape of the wearer. English knitting is great for more rigid, tighter knits where the final shape of the knit piece of fabric is more important, as in outer coats and stuffed toys. Changing from one style to another can also correct tension and gauge problems, if changing needle sizes isn't quite doing the job.
As you widen your knitting repertoire, you may find patterns calling for the style you're not familiar with. If you're not ready to learn or don't have the inclination to, don't worry – the style of knitting you use won't be enough to make a complete mess of a given pattern. You can use either Continental or English knitting to knit anything without fear of ending up with a completely unusable piece. It's only important when you get to the point where you're interested in altering the very finest details of your knitting.
It's not really fair to set up a comparison in terms of English vs. Continental knitting, because over the course of your knitting career it will be useful to at least have a working knowledge of both stitches. Whilst you can get similar results with both styles, they'll never be exactly the same, and it's always good, once you get to a certain skill level, to have a grasp of both so you can get precisely the results you're looking for.