Threat is anything that forces your opponent to make defense, but doesn't actually deal damage, at least not without you paying an additional cost. Drake is an example of a threat unit: paying 12
for just two damage a turn is very inefficient, however Drake also threatens to deal 2 additional damage by clicking, so your opponent must make 2 more defense even though you probably don't want to click your Drake.
Threat can be played around by vigilant units, that is, units that can block and do something else at the start of a turn. For example, a Xeno Guardian can attack at the start of your turn and still be used in defense that turn. Normally this isn't too useful because if you sacrifice it in defense then it stops attacking. However, if your opponents has an Odin and you have an extra Xeno Guardian (besides the one you're absorbing on), they won't want to give up the defensive value of absorbing on their Odin, so your Xeno Guardian can continually act as both 
4 of defense and a constant attacker simultaneously - it's like you payed a mere 5
for an Infusion Grid and a Gauss Cannon. That's a bargain! And the only way your opponent can put an end to this mad value is by clicking the Odin and thereby losing defensive value themselves.
Many chill units are also a form of threat, such as Frostbite.
Threat is also completely useless against breachproof opponents.