The queen of the gods absolutely despises Heracles, because he is yet another reminder of her husband Zeus' cheating, philandering ways. Most of the time, Hera takes out her anger on Zeus' many mistresses, but instead of lashing out at Alcmene, Heracles' mother, the Hera focuses all her venom on Heracles. (Well, Hera did try to kill Alcmene by attempting to stop Heracles' birth, but after that the goddess left the woman alone. For Hera, that's downright generous.)
There's no real explanation as to why Hera hates Heracles, in particular, quite so much. Is it because he got a free sample of her breast milk thanks to Athena? Maybe. Is it because Heracles is kind of named after her, and she's not even related to him? Perhaps. More than likely it is because he's the shining star of all of Zeus' illegitimate children. Every time Heracles slays another monster, it probably ticks Hera off just a little bit more. Whatever the reason, pretty much every myth agrees that Hera had a special kind of hatred for the Heracles.