In a convex lens (sometimes called a positive lens), the glass (or plastic) surfaces bulge outwards in the center giving the classic lentil-like shape. A convex lens is also called a converging lens because it makes parallel light rays passing through it bend inward and meet (converge) at a spot just beyond the lens known as the focal point.
A concave lens is exactly the opposite with the outer surfaces curving inward, so it makes parallel light rays curve outward or diverge. That's why concave lenses are sometimes called diverging lenses. (One easy way to remember the difference between concave and convex lenses is to think of concave lenses caving inwards.) Concave lenses are used in things like TV projectors to make light rays spread out into the distance. In a flashlight, it's easier to do this job with a mirror, which usually weighs much less than a lens and is cheaper to manufacture as well.
The major difference between concave and convex lenses lies in the fact that concave lenses are thicker at the edges and convex lenses are thicker in the middle. These distinctions in shape result in the differences in which light rays bend when striking the lenses.