Energy Resistance reduces the damage you take from that energy type. With Fire Resistance 3, you subtract 3 from fire damage you take.
There is some confusion, however, about how often this works. The Resistance to Energy special quality states that
A creature with resistance to energy has the ability (usually extraordinary) to ignore some damage of a certain type each round, but it does not have total immunity.
(emphasis mine) Here, you can subtract 3 from the total amount of fire damage you take each round. However, the resist energy spell says this
The subject gains energy resistance 10 against the energy type chosen, meaning that each time the creature is subjected to such damage (whether from a natural or magical source), that damage is reduced by 10 points before being applied to the creature’s hit points.
(emphasis again mine) In this case, it’s not 3 subtracted from the round’s total fire damage, but 3 subtracted from every instance of fire damage. This is obviously quite a lot stronger.
The Rules Compendium clarifies this situation:
A creature that has resistance to energy has the ability (usually extraordinary) to ignore some damage of a certain energy type each time it takes damage of that type.
(emphasis yadda yadda) So with Rules Compendium it always applies each time. However, you will need to double-check with your DM on this, because A. Rules Compendium is a supplement, and B. the errata rules do not actually allow Rules Compendium to change the rules in the PHB, so your DM will have to OK it.