What is the difference between a determinate and an indeterminate tomato?
The terms refer to the growth habit of a particular variety (and there are also semi-determinates). Think of determinate and indeterminate like bush types and vine types.
Some varieties grow to about 3 feet and then stop, making them ideal for gardens with restricted space or container use. These are the determinates. Indeterminates, which includes many of the heirloom types, grow like the vines they are, as long as the season will allow.
Another difference is that generally speaking the relatively short branches of determinate plants end in a flower cluster, and most of these ripen in the same several-week-long period (a good trait if you want to make one giant harvest into quarts of sauce, for instance). With indeterminates, more potential flower-cluster-bearing growth is produced as long as conditions allow, so there are multiple harvests over a longer season.