An auxiliary expression attached to a verb stem meaning that something ought to be done, is desirable, or is expected (should/ought to).
彼はすぐに謝るべきだ。
He should apologize immediately.
この問題は早く対処するべき問題だ。
This is a problem that should be dealt with quickly.
やるべきことをリストに書いておこう。
Let's write a list of the things we should do.