What's the word for "tiny pieces of food stuck in between teeth"?

According to Mosby's Dental Dictionary and as suggested by Jim in the comments, the term is food debris:

Particles of food remaining in the mouth after eating which collect in tooth crevices and between the teeth and may contribute to the formation of dental caries.

A proper answer (food debris) has already been given; not right, but related, and suitable for extreme circumstances, is gobbet:

1. a quantity of liquid, often in a sticky blotch
2. a lump or chunk of something, especially of raw meat

In informal use, I believe there is not a specific word for this. Most people would just say "I/you have something stuck between your teeth."

The following single words are also frequently used to describe food that is stuck between the teeth.

Remnant:

a usually small part, member, or trace remaining

Residue:

something that remains after a part is taken, separated, or designated or after the completion of a process

Remains:

a remaining part or trace —usually used in plural