The simply answer is that your A/C dumps heat outside using big metal fins, it’s not terribly great, but it works well at that scale.

Dissipating it into the air for the amount of heat some data centers need to get rid of doesn’t cut it, so they use evaporative coolers.

The phase change of evaporating water from liquid to gas uses approximately 7x more heat energy than taking room temperature water and getting it up the boiling point itself.

Essentially they stick their large metal fins from the AC into a large pool of water and boil it off. This gets rid of the energy with a much smaller and cheaper system, but uses up water.