と has a lot of uses.
As far as I know, と can be uses to point to:
- a member of a complete list (X と Y と Z => noun X AND noun Y AND noun Z)
- a cause of a natural consequence (condition A と natural consequence B => ALWAYS WHEN condition A THEN consequence B)
- a partner also doing the action (person A と action Z => to do action Z TOGETHER WITH person A)
- with certain type of adverbs (the so called "adverbs taking the 'to' particle"), for example しっかり、だんだん etc.
- a quote (X と [person A は] said => "X" said [person A])
The と used here is a quotation particle:
~~と言う
=> to say that ~~
~~と約束する
=> to promise that ~~