If something is feasible, then you can do it without too much difficulty. When someone asks "Is it feasible?" the person is asking if you'll be able to get something done.
Feasible things are possible. If you have enough time, money, or energy to do something, it's feasible. Something might be feasible at one time and then not feasible at another time. Because of technological advances and competition with the Russians, going to the moon was feasible for the United States in the sixties. Often, people disagree about what's feasible, especially in politics, where how feasible a project is counts for a lot.