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, a card like Clever Hobbits (7U54) would be called "Ninja Gollum hate", because they are very effective in one matchup but of limited use in other matchups. One might also refer to "condition hate" or "possession hate" as a means of countering particular card types useful in more general 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 Silver Bullet is an extremely narrow hate card designed with the purpose of sniping one particular card or strategy (the way a silver bullet is a counter to Werewolves and not much else). Terrible as the Dawn (3R103) is among the most notorious examples thanks to the later prevalence of Galadriel, Lady Redeemed (10R11) . Other early silver bullets include Too Great and Terrible (3R85) , Can You Protect Me From Yourself? (3R50) , Such a Little Thing (3R80) , and (ineffectually) The Weight of a Legacy (1R282) . Gríma, Wormtongue (4R154) is a more general hate card against any deck that tries to build up several cards on a companion (a strategy very prevalent early in the game), but in later metas it can be considered a sort of silver bullet against Durin III, Dwarven Lord (9R+3) as one of the few companions that still attempts that strategy. Similarly, Stand Against Darkness (1U63) might be included not for its general Sauron hate, but specifically to counter Grond, Hammer of the Underworld (8R103) and Sauron, The Lord of the Rings (9R+48) .
(Decipher was (in)famous for using such silver bullet cards, especially in the Star Wars CCG where they never banned cards and instead opted to release silver bullet counters. This habit carried over into the LOTR-TCG, but it was mostly phased out as a design strategy after the introduction of the X-List.)
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.