Life is essentially lots of different chemical reactions. Those chemical reactions which are to do with life are called biochemical reactions. If you map how one compound reacts with another in a series of bichemical reactions the result is a biochemical pathway. A very famous one is glycolysis where glucose is gradually broken down through a number of steps into acetyl coenzyme a.
Enzymes, BTW, are the biological catalysts that help the biochemical reactions occur. So, in the 10 (or so) steps in the glycolytic pathway there are 10 (or so) different enzymes: each one catalysing one particular step.