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Rennet
Rennet is an enzyme used in cheese making to curdle milk. That reaction makes the proteins and water break apart into curds and whey. Traditionally it comes from the stomach linings of ruminant animals such as cows, goats and lambs, but there are vegetarian kinds too: microbial rennet (made from molds or other microbes), fermentation-produced chymosin (the same enzyme, made by cultured microbes instead of taken from an animal), and vegetable rennet from plants such as thistle.
To tell whether a cheese is vegetarian, look for "vegetarian rennet" or "microbial enzymes" on the label. A label that just says "enzymes" or "rennet" doesn't tell you.
You can order rennet tablets online, including vegetarian rennet (Amazon).
Annatto
Annatto is a natural dye collected from the pulp of the seeds of the achiote tree. It's orange-red, and it's used in some cheeses for color rather than flavor (it adds little to none). You'll find it in cheeses like cheddar, Colby, Red Leicester and Mimolette.