Stance is a general MMO term used to describe... man this is going to be tough to explain.
I'll give example to help try illustrate. With my Sith Marauder I have the ability to use different lightsaber combat forms. There's the Shii-Cho Form and the Juyo Form and my personal favourite, the Ataru Form. These are all "Stances" which you can only equip one at a time... they'll have different names for different classes. For example I mentioned the Ion Cell with my Vanguard which is a stance used for Tanking.
But going back to the Marauder, the Shii-Cho, Juyo and Ataru Form all have different abilities they bring to your character.
The Shii-Cho Form slightly increases both damage dealt and reduces damage recieved by 3% and is considered a balanced stance.
The Juyo Form is a more offensive stance that stacks 2%damage every 15 seconds up to 5 times. So basically it causes damage to occur over time.
The Ataru Form is another offensive stance but is different from the Juuo Form because instead of causing damage over time, the Ataru Form deals direct damage to the target. Using this form also increases your accuracy by 3%.
So difference stances do different things and the abilities you choose on your skill tree are sometimes based on these stances and will say so when you hover over them.