Hate is an informal game term referring to the card or group of cards you build into 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 include cards which 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 (also called a silver bullet) is an extremely narrow hate card, especially one that targets a particular opposing card by name. Too Great and Terrible (3R85) is among the most notorious examples thanks to Galadriel, Lady Redeemed (10R11), while Stand Against Darkness (1U63) is included in decks specifically for Grond, Hammer of the Underworld (8R103) and Sauron, The Lord of the Rings (9R+48). Some cards are magic bullets in certain matchups and not others: Gríma, Wormtongue (4R154) can be a magic bullet against a deck built around Durin III, Dwarven Lord (9R+3), but more broadly just hate for other decks that would be tempted to stack 3 or more cards on a companion. Decipher was (in)famous for such cards, in this game and their other games, and they are most 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. A hard counter is very effective and tends to be more focused, while a soft counter offers only a limited benefit against a particular strategy, deck, or card at the benefit of being more generally useful. A single card can fit into either of these categories depending on the situation: Sleep, Caradhras (1C84) is a hard counter to condition-heavy strategies such as Sauron Grind and a soft counter to a Nazgul beatdown deck with Blade Tip (1U209) and Black Breath (1U207). For grind losing all conditions before the last few sites almost always means losing the game, while for Nazgul it typically means killing companions more slowly.