A threat is something that if not dealt with will cause a player to lose. Answers deal with threats, while chump blockers delay the loss, provided the threat comes in the form of a creature. Strategically, the choice of threat is indicative of the game plan that a deck is designed to execute.
There are many forms of threats, but for any real game of Magic, many permanents are threats while most instant and sorcery spells are answers, as permanents can cause a continual influence on the game. That said, to constitute a threat, it must attack a resource. For most forms of Magic, advantages are zero-sum; to generate an advantage on one side is to cause a deficit on the other, so perpetual generation of resources will also constitute a threat. At the greatest extremes, an effect that stops its controller losing (most famously, Elixir of Immortality in Pro Tour Magic 2015) will eventually force the opponent to draw from an empty library.
Creatures tend to be the most common threat by their basic operation of attacking life totals. Planeswalkers are usually threats by generating card advantage. Other effects are more nebulous as to why they are threats, usually through the architecture of their decks, such as Lantern Control. On the other hand, the main reason instants and sorceries are rarely considered threats is that it is fairly difficult to prevent their resolution, so their power is diminished.
Competing threats are often judged by their clock, or the turns it takes for them to end the game. An enchantment that mills two a turn will take something from fifteen to eighteen turns to kill, whereas a three-power creature will kill in seven turns. This is the basis of goldfishing; killing an opponent with no resistance. On the other side of judging is their resilience; the creature is likely to not hit more than five times for various reasons (blockers, removal) after which the opponent will not lose to it; in contrast, the milling enchantment is much harder to interact with and even if removed after fourteen turns, the opponent may still deck in six more. Balancing these two is the fundamental deck building question.