Definition of speech
Check is the equivalent of a check. When it's our turn to play on a street (flop or turn or river) and no bet has been made yet, each player has the option to fold or bet. Fold is the equivalent of making a bet of 0. Some players will say "check", others "pass" and still others "call". The term "check" may also be used to signal to a player that it is their turn to play. Other casino dealers will say "options, check or bet". If a player bets after we have passed (by saying "check"), the options return to us and we must call the bet, fold or raise.
Is passing a sign of weakness?
When a player says "check" to pass, it is not necessarily because he is weak. He may fold because he is preparing to call a bet and does not want to inflate the size of the pot too quickly. He may pass because he has a weak hand and is preparing to fold against any bet, but he may also be preparing to check-raise (call with the intention of raising if a player bets). The check-raise allows us to put more money in the pot on a particular street (more than if we had just bet).