A factor is a part or element that contributes to a result. If you only fly budget airlines and refuse to stay anywhere but youth hostels, then money is probably a big factor in your travel plans.
The word factor doubles as both noun and verb. A factor is an element that influences something, like many factors that contribute to global warming. To factor means to consider something relevant when making a decision or conclusion, like factoring in the weather and traffic when figuring out how long the drive will be. And if it's not relevant? Then you factor it out.