Heirloom tomatoes are varieties that have been saved and passed down through the generations.  Heirlooms generally are lower yielding than modern hybrids.  The thin skin that contributes to their flavor also means that they will crack more easily than thicker skinned varieties.  Despite these characteristics, you will not find a better tasting tomato than an heirloom.
 
Determinate varieties are bush types that grow to a certain size and then put their energy into ripening fruit.  Fruits ripen over a more concentrated period of time allowing 1 or 2 main harvests which is particularly good for canning.
 
Indeterminate varieties are the vining types that continue to grow until frost.  They require more elaborate trellising methods to contain the large plant and more labor to sucker and prune.