It is not possible to make a break in snooker more than 147. But it is possible to end the game with a score higher than 147 if you opponent made a foul shot before a red has been potted.
Reds are worth one point, yellow two, green three, brown four, blue five, pink six and black seven. Each red potted stays down and red must always be followed by a 'colour' ie anything not red. After the reds are all potted, the colours must be potted in sequence.
A 147 break is when each red is followed by a black. Since there is no ball with a higher point value 147 is, as it is often known in competition the 'maximum break'.
However if your opponent fouled before a red was potted you would have a number of points (depends on the type of foul- if a blue was illegally potted by your opponent you would gain 5 points and the ball would be returned to its spot.)
But that doesn't mean you have a higher break, just a higher score at the end. (A break always refers to the score accumulated on the turn until you play a safety, miss or otherwise foul.