The pitcher who allowed the runner to reach base that scored the run that put the opponent team ahead for the rest of the game is tagged with the loss. Once a pitcher's team reties the game, he's "off the hook" for the loss unless he once again allows the lead run that holds up for the rest of the game. An important distinction is that the pitcher who put the runner on base gets the loss, rather than the pitcher who allows the hit that scores the run.
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The losing pitcher is the one who is responsible for permitting the opponent who scores the winning run to get on base. The "winning" run is the one that gives one team the lead that it never relinquishes.
Examples:
1) A starting pitcher for the home team gives up one run in the first inning, then shuts out the visitors until he is removed after the 8th inning. His team, however, fails to score a run through these same eight innings. Relievers come in for the top of the 9th and give up nine runs, making the score 10-0 going into the bottom of the 9th. The home team scores "only" nine runs in their half of the last inning, thus losing 10-9. That one run in the first inning was thus the "winning" run, and the starter gave it up -- so he's the losing pitcher.
2) Score tied, bottom of the 9th, bases empty. Pitcher gives up a bloop single and, when the manager notices that this pitcher is getting tired, he takes that pitcher out of the game. Because that pitcher gave up the hit that caused that batter to get on base, that pitcher is "responsible" for that base runner.
The following reliever thows 12 straight balls, walking in the winning run. Because the batter who scored that winning run got on base because of that first pitcher, that first pitcher is "responsible" for the winning run, and is thus the loser. The fact that the reliever was clearly the one who pitched worse in that inning is irrelevent.