Pragmatism is a philosophy (or anti-philosophy). Like consequentialism 
, it cares about the consequences of actions. Unlike utilitarianism , consequentialism's bastard offspring, it's not weirdly obsessed with quantification.
Perhaps the big difference between pragmatism and consequentialism is that consequentialism sees itself as a method to resolve arguments, whereas pragmatism is happy to let some issues remain unresolved. (See Consequences of Pragmatism.)
To my mind, the core of pragmatism comes from William James, who called it a "method for settling metaphysical disputes that might otherwise be interminable." His famous maxim is that unless some "practical difference would follow from one or the other side's being correct, the dispute is idle."
I saw an example once on a consulting trip with Ron Jeffries. A meeting with a team was getting a bit heated, with one person pushing back on abstract points. Ron said something like, "If you're right, how would we behave differently than if I was right?"
That's a Pragmatist question, a good one to keep in mind during arguments.