The anchor date, more commonly just called your SIP date, is the specific day of the month — say the 5th or the 15th — that you choose when setting up your SIP, on which your fixed instalment amount is automatically debited from your bank account and invested into the chosen fund each month.
While in theory the exact date shouldn't matter much over a very long investment horizon, since it's just one of roughly 20-22 possible trading days each month, some investors choose their SIP date to align with their salary credit date, ensuring sufficient funds are available in their account and reducing the chance of a missed instalment due to insufficient balance.
If a chosen date falls on a weekend or holiday, the debit is usually processed on the next available working day, so there's no need to worry about exact calendar precision.