In formal logic, a premise is a plank of an argument. If your premises are true and the form of your argument is valid, then your argument is sound.
1. All men are mortal.
2. Socrates is a man.
3. Therefore, Socrates is mortal.
If you're trying to persuade someone of your conclusion ("Socrates is mortal"), you're not going to get anywhere if they don't already agree with your premises ("All men are mortal" and "Socrates is a man"). The premises are the common ground on which you can meet your opponent and find what you can agree on.
If you can't find any common ground-- that is, agree on the premises-- then you might as well not bother arguing. If you can find the common ground, then you have hope that your opponent will go along with you to your conclusion. Opting to shout across a chasm instead is a pastime that many people find satisfying for reasons that can be discussed elsewhere, but this is the real substance of argument.