Definition of check/call
A check/call is checking with the intention of calling if a player bets in position on us. Telling yourself that you are checking/calling is thinking one move ahead. There are several reasons to check/call. One reason to check/call is when you have a draw. We can also check/call when our opponent is in position on us and likes to bluff. In short, you can check/call for any number of reasons.
2 examples of check/call
The check/call is always done out of position. For this reason, both examples will be out of position. In situation number 1, we have 8-9 in heart over 9-9-8. Here, betting could cause our opponent to fold. With a hand this strong, we want to keep him in the hand. Check-raise would show too much strength and again, our opponent might fold. The most logical option is to check/call. We check in turn with the obvious purpose of calling against a bet.
For example number two, you have 8-9 in hearts still, but on A-2-5 with two hearts. In this situation, out of position, if we bet and get raised, we are in a bad situation. Check/call seems more appropriate.