When faced with an poker tournament opponent that bears a great hand, it is important to follow some basic strategy so you don't get eliminated. Obviously what to do depends on what hand ranking that you have.
In poker tournaments, players play a tighter poker game than usual, mainly because of fear of going broke and losing the poker tournament. This means that players will raise and bet, with lesser hands than they used to, in regular poker games.
Once you are playing in the poker tournament, and you notice a player raising, it will mean he has a fairly good, and quite possibly a great poker hand. In this situation you might find yourself in a poker tournament game, with money you've placed already in, and facing an opponent that almost assuredly has a better hand than yours. This can be of course quite frustrating for the novice player, but could be handled if properly prepared for.
If you have a fairly good hand, then in cases your opponent raises or even calls, it may mean his hand is better than yours. This situation often arises in poker tournaments, even without you expecting it. One option for dealing with an opponent with a strong hand is to sandbag, meaning to play your hand as if it were a better one. This way the opponent will think you have a better hand that you actually do and will possibly fold.
If you have an excellent hand, then there is a good chance, that your hand is superior to your opponent's, even though your opponent bet his hand. In this case you should keep checking at every round, so the pot can become larger, and so that players won't suspect you have a great hand and fold. Then again he could be bluffing.