Overtricks are very important in matchpoint bridge.  If a player plays to 'make' his contract first and only after making the contract he or she will frequently score 420 while others are scoring 450.
A matchpoint player must constantly play for overtricks. He must even sometimes risk his contract to make an overtrick. However he should not foolheartedly try for overtricks. A reasonalble expectation of success must exist before risking one's contract for an overtrick.
Some guidelines:
Risking your contract by finessing into the opponent who has shown the strongest hand. Finessing into the weaker hand has a reasonable chance for success.
If a player plays the A, K, Q of hearts with dummy and the other opponent having three and you have two andhe has not bid, the chances are he will not hold the club king.
If a player passes his partner's opening bid (1  P  P) and plays an ace the chances are he will not have much more in honor values.

Example One:
NORTH J1087 AQ A654 975            

SOUTH KQ96  5  832  A8642          
SOUTH  WEST  NORTH  EAST              
Pass   1    Pass   2              
Double Pass  2    Pass               
Pass   Pass
In example one East leads the K.   North must go to the A at trick 2 and take the spade finness. If it wins North then cashes the A and pitches a diamond. The spade finness has a 75% chance of winning - making 3. Making only 2 will be a bad result.
NORTH 76    752  KQJ7   KQJ7

SOUTH AQ43  AQ4  8432  A5

 1NT   Pass  3NT    Pass
 Pass  Pass
In example two West leads the 5. South plays two rounds of diamonds. The second won by West who plays the 2. South cashes the clubs and diamonds. East shows out on the third round of clubs. It is likely that East has zero, one or two hearts so South should take the heart finess to try for an extra overtrick