In no-limit hold’em, it is a common strategy for the pre-flop raiser to fire a continuation bet on the flop. An opponent with a strong hand will often check quickly to the pre-flop raiser, because they don’t want to prevent the pre-flop raiser’s natural tendency to fire another round. They don’t want to arouse suspicion by taking a long time to check.
An immediate (and by immediate I do mean immediate, as in a second or less) check from a player first to act would probably arouse my suspicion. (This is assuming that the player usually takes longer to check when he is weak–that’s something you have to correlate first, because some players routinely check very quickly and you need to notice who those players are.) The larger the pot, and the weaker your opponent, the more a quick first-to-act check should worry you.
An immediate check from a player who is last to act is not as worrisome. Oftentimes the player last to act is just grateful to have gotten a free card and isn’t thinking too much about his image or how his image may be interpreted.
A weak player last-to-act who takes a long time and then checks is similar to the first-to-act player who does the same thing. He often wants to make his opponent(s) think he contemplated a bet but changed his mind.
Combined with other tells, bet-timing tells can be very revealing. Let’s say the river card has just arrived in a heads-up pot that’s pretty substantial. Your opponent stares at you while it’s your turn to bet (which we know can often be a sign of weakness for some players). You check to him and then he takes a long time to check. For most players, this will mean they don’t have a hand.
Or let’s say instead that the same player checked instantly to you on the river. You study him; he doesn’t look at you. Instead, his gaze is focused on the table. These two factors (his speed in checking and his demeanor) might influence you to check behind.