Ennis Del Mar and Jack Twist are a couple of good ol' country boys: strong on work ethic, weak on schooling. They get paired together in the summer of 1963 to herd sheep up on Brokeback Mountain. One thing leads to another, and the intimacy of their work eventually leads to a night personal intimacy (which is a bit of a surprise to both of them, since neither one considers himself gay.) They keep up an affair until summer ends and they go their separate ways—even though it's clear that their love is pretty doggone real.
Four years pass. They get married and have kids, all without seeing each other. Then Jack shows up at Ennis's door one day and soon enough, they're in a passionate embrace… which Ennis's wife witnesses. They try to blow it off and she doesn't ask, but some things can't be unseen, and the gents excuse themselves to a motel where the affair begins anew.
Sporadic motel meetings and camping trip trysts continue for the next 20 years. It eventually drives Ennis's wife away, but Jack's family stays together, even though his own wife Lureen clearly Knows What He Did That Summer (and every summer thereafter). Eventually though, the fact that they can't be together starts to catch up with Jack, who can't keep his feelings to himself the way Ennis can.
Sadly, Jack dies when his "tire blows up," which Ennis thinks is code for "Jack got beat do death in a hate crime." He talks to Lureen about it on the phone, then goes to Jack's parents' house to try and talk them out of Jack's ashes. (Jack wanted them buried on Brokeback Mountain.) Ennis can't convince them to part with the ashes, but he finds a pair of shirts that Jack wore on Brokeback and makes off with them as lovely parting gifts.
He hangs the shirts in his trailer, along with the postcard of Brokeback. The memories are painful, but they're all he has.