A Nuke (or "Field Clearer", etc.) is an unofficial term used to describe the action of a card effect with the power to destroy a large number of cards on the field. This term also applies to cards that destroy all monsters or Spells/Traps exclusively, such as "Dark Hole" or "Heavy Storm". Cards that can destroy a big number of cards, but only destroy a small number when used, aren't referred to as a nuke. For example, if a player activates "Dark Hole" while their opponent controls just one monster, it wouldn't be considered a nuke. The term goes to the situation, not the card.
The first card released with this kind of effect was "Final Destiny", with an extremely high cost. This term is usually only assigned by the speed of which the card(s) manage to destroy all cards on the field. For example, even though "Harpies' Hunting Ground" is capable of destroying all of your opponent's Spell/Trap cards, it will only destroy one every time you Normal/Special Summon an "Harpie", so since it can be completely stopped by a single Spell/Trap-removal card, it isn't considered a nuke.
Usually, cards with a nuke effect will have a big restriction/cost/downside/specific activation time for using the effect. The effect of "Evilswarm Exciton Knight", a monster that can be Summoned using just 2 Level 4 monsters, can only be used while your opponent has more overall cards in their hand and field, and will also give your opponent immunity from damage for the rest of the turn. The above-mentioned "Final Destiny" also required you to discard 5 cards. This rule is sometimes broken and the card doesn't have a major downside, the most infamous example being "Raigeki".