Determinate varieties of tomatoes, also called "bush" tomatoes, are varieties that are bred to grow to a compact height (approx. 4 feet).
They stop growing when fruit sets on the terminal or top bud, ripen all their crop at or near the same time (usually over a 2 week period), and then die.
They may require a limited amount of caging and/or staking for support, should NOT be pruned or "suckered" as it severely reduces the crop, and will perform relatively well in a container (minimum size of 5-6 gallon). Examples are: Rutgers, Roma, Celebrity (called a semi-determinate by some), and Marglobe.
Indeterminate varieties of tomatoes are also called "vining" tomatoes. They will grow and produce fruit until killed by frost and can reach heights of up to 10 feet although 6 feet is considered the norm. They will bloom, set new fruit and ripen fruit all at the same time throughout the growing season.
They require substantial caging and/or staking for support and pruning and the removal of suckers is practiced by many but is not mandatory. The need for it and advisability of doing it varies from region to region. Experiment and see which works best for you. Because of the need for substantial support and the size of the plants, indeterminate varieties are not usually recommended as container plants. Examples are: Big Boy, Beef Master, most "cherry" types, Early Girl, most heirloom varieties, etc.