An assumption is a premise that is unstated or hinted at in the argument and on which a conclusion is based. In GMAT, one of the ways to challenge an argument is to attack the validity of the assumptions.

For example:

Sleep deprivation leads to obesity (Premise 1)
Peter Parker is obese (Premise 2)
Therefore Peter Parker is sleep deprived (Conclusion)

The assumption is that there can be no other cause of obesity/Sleep deprivation is the only cause of obesity.

Here is another example:

More than 40 percent of a sample of amphibians, reptiles, mammals, and birds that are restricted to mangrove ecosystems are globally threatened with extinction, according to an assessment published in the July/August issue of BioScience. Unless shrimp farming is restricted, prospects for mangrove-restricted animals are bleak.

The assumptions here are: 1) Shrimp farming contributes to the destruction of mangroves and 2)The only threat to mangrove ecosystems come from shrimp farming.