Definition
A selection a punter feels very confident about and builds a bet around, often used as the fixed selection in a system bet or included in every accumulator.
"Banker" is everyday betting slang, not an official market. Calling a selection a banker does not change its odds or how it is settled: it is still an ordinary selection that can lose.
The danger with bankers is that people repeat the same selection across many slips. If that one result goes wrong, every slip that contains it loses together. Short-priced favourites lose more often than people expect. A team priced at 1.25 is, by the bookmaker's own estimate, beaten or held to a draw roughly one time in five.
In a system bet, some bookmakers let you mark a selection as a banker so that it appears in every combination. That increases the possible return if it wins, and makes every combination depend on it.
Before treating anything as a banker, convert the odds to a probability with the implied probability calculator, and keep stakes within your bankroll plan.