Whenever the data changes "significantly".
If a table goes from 1 row to 200 rows, that's a significant change. When a table goes from 100,000 rows to 150,000 rows, that's not a terribly significant change. When a table goes from 1000 rows all with identical values in commonly-queried column X to 1000 rows with nearly unique values in column X, that's a significant change.
Statistics store information about item counts and relative frequencies -- things that will let it "guess" at how many rows will match a given criteria. When it guesses wrong, the optimizer can pick a very suboptimal query plan.