Definition of cooler
A cooler is when a very strong hand meets an even stronger hand. A cooler is a situation that cannot be avoided. If two players in the blinds have a pair of kings and a pair of aces, there is a good chance that both players will be all in preflop. This is called a cooler. A cooler is a foregone conclusion. There are some situations in poker that are almost inevitable. If I have AQ on A-A-K-Q-2 against a very aggressive player and I lose all my money to his AK, it's simply a cooler. The expression could be translated as "a shower of cold water".
A cooler is not a badbeat
There is a distinction between the two terms. A badbeat is when we bet all our money before the river as a heavy favorite. Badbeat is when very unlikely cards will give the pot to our opponent. If I call an all in with a pair of 2's to AA on 2-2-5 and the turn is an A and the river is another A, then I am said to have badbeaten. If the all in was on the river instead of the flop, then we can call it a cooler.