Pascal's Wager (or Pascal's Gambit) is the name for an idea that Blaise Pascal had. He said that it is not possible to prove or disprove that God exists. Therefore, it is better to bet that God exists. If God existed, and the person believed in God, he would be rewarded (with happiness forever); if the person did not believe, he would be punished (with what is called eternal damnation). If God did not exist it would make no difference. For this reason, it would be better to believe in God, Pascal said. Indeed, Pascal strongly believed in this ideal. 

Pascal's argument is a simple one: reason and intellect cannot decide the question of whether God exists or not; therefore, it makes sense to choose the option that would benefit us most should we be right.  Accordingly, the options would be as follows: 

1. You may live a religious and moral life and be rewarded by eternal happiness.

2. You may live a pleasure-seeking life and be denied eternal happiness.

3. You may live a holy life but there is actually no God or eternal life.

4. You may live a pleasure-seeking life but it makes no difference because there is no God. 

For Pascal, the first of these options is the most important one because it represents the maximum gain and loss. Even if it should turn out that there is no God, the sheer risk of deciding against such a possibility warrants that we should take that option.

The case against Pascal's Wager
The argument from inconsistent revelations shows we have no idea which hell to avoid since many different religions exist with different beliefs about hell.  Within religions there are different denominations and sects with different ideas about heaven and hell.  If we try to avoid the hell that Christians believe in we are at risk from the hell Muslims believe.  So it goes on.  Perhaps God does not like people who accept Pascal's Wager but god may not mind that atheists doubt.  Atheists and believers could both be in trouble or neither could be in trouble. 

A moral and loving god that deserves respect will not mind when people doubt and do not believe in it for rational reason.  Such a god will not punish us for critical thinking or for doubting statements from other imperfect human beings. 
A moral and loving god that deserves respect will disapprove when believers accept immoral acts that are in religious texts.  One example is Abraham being ready to sacrifice Isaac in the Old Testament. A good god would want Abraham to value compassion more than fear and loyalty and to spare Isaac.  A good god would reward Abraham for sparing Isaac.  A moral and loving god that deserves respect will condemn very many cases of genocide also in the Old Testament and will disapprove when believers imagine genocide can be moral. 

Further two of the three Abrahamic religions, Christianity and Islam claim worshiping other gods is sinful. Judaism, however is different, being older and clarifies that as long as you acknowledge the existence of the G-D of Abraham, and don't blaspheme the name, you do not need to worship any deity, and may worship any you like. The loss of understanding and ignoring the Noahide Laws has muddled the issue.

We have no proof that any particular deity is real, but as there is no wrong deity as long as you acknowledge the Abrahamic one, meaning Paschal's Wager stands, belief is the only safe bet.

Importance in history
Pierre de Fermat and Pascal created probability theory. Pascal's Wager was very important for the time, because it did new things with probability theory. It is also one of the first tries to use the concept of infinity, and the first use of decision theory. It was important for other philosophers who developed the ideas of pragmatism and voluntarism.

References 

Philosophy