Something is finite if it comes to an end. (Like this Algebra study guide, believe it or not.) A book or movie is finite: after you've turned the last page or watched the final credit, it's over. A day is finite: after 24 hours, the clock calls it a wrap and starts over with a new one. Your body takes up a finite amount of space: you have skin (hopefully on the outside), and there your body ends.
Something is infinite if it does not have an end. Infinity is not a number but a concept. The counting numbers, for example, are infinite: if you start counting and try to count as high as you can, you'll never finish because you'll never run out of numbers. Unless you can only count to 100, in which case, jolly good show.
Fractals are also infinite: no matter how much you zoom in, you can always zoom in more.
For those who like silly books, The Phantom Tollbooth has a wonderful description of infinity in Chapter 15, "This Way to Infinity." You can also try David Foster Wallace's Infinite Jest, which is so lengthy it's also almost an "infinite read."