Hate is an informal game term. Hate is the practice of building your deck to counter a strategy you expect your opponent to use, and it's used both in the general sense and the specific sense. In the general, "the meta has a lot of hate for Corsairs," means that there are many decks that counter Corsair decks in the metagame. In the specific, cards like Clever Hobbits (7U54) are often called hate cards, because they are very effective in one matchup (in this case Ninja Gollum), but of limited use in other matchups.
Tech is a synonym for hate, and is often used in the general ("tech against the Movie Block meta") or the specific ("Clever Hobbits is a tech card"). It's also used as a verb ("teching against" a strategy). This usage comes from the fighting game community, where originally referred to attacks that cancel out or interrupt other attacks.
A magic bullet is a narrowly-targeted hate card, often one that targets a particular opposing card by name. For example, Too Great and Terrible (3R85). Decipher was (in)famous for such cards, in this game and their other games, and they are common in early sets.
Counter is another synonym (although that word may also be referring to tokens). A counter card and a hate card are the same thing. Counterplay is a strategy that works against a particular opposing strategy, and often involves playing particular hate cards. A hard counter is very effective, while a soft counter offers only a limited benefit against a particular strategy, deck, or card.