Who was Pompey?
Pompey, or Pompey the Great, was a well known military leader of Rome. He never appears in Shakespeare's play, as he's just been defeated by Julius Caesar in battle. So he's not really very relevant, unless you're reading the first two scenes.
But here's the history on him. He was initially an ally of Caesar's, and of another well-known politician called Marcus Crassus. They were the "First Triumvirate" (the second, of course, is Antony, Octavius and Lepidus after Caesar's death). Crassus died, and then Pompey and Caesar began to argue about the way power was shared in Rome. They eventually became rivals in a civil war. Pompey was defeated by Caesar at the Battle of Phrasalus in 38 BC. It was a decisive victory for Caesar, and Pompey had to run for his life.
And here's his mention in the play:
Knew you not Pompey? Many a time and oft
Have you climb'd up to walls and battlements,
To towers and windows, yea, to chimney tops,
Your infants in your arms, and there have sat
The live-long day with patient expectation
To see great Pompey pass the streets of Rome.
The tribunes are angry with the commoners for celebrating Caesar's victory when, only a short time before, they were celebrating Pompey. Crowds, indeed, are fickle.