How common something is across a relevant population or stretch of time, before adjusting for anything specific to the case in front of you. If roughly 1 in 365 birthdays fall on a given day, that’s the base rate for “was born on that day” — the starting point before you ask anything more specific about the person.
Choosing the right base rate means choosing the right reference class — the group of comparable people, events, or occasions the case is really being compared against. Picking too narrow or too flattering a reference class, often without noticing, is one of the most common ways a coincidence ends up sounding more improbable than it is; see step 6 of how to evaluate a coincidence claim.