All air conditioners create condensation (i.e. - water) as a byproduct of cooling. The way they cool down your house is by reducing the interior humidity. Dehumidification creates water, and that water has got to go somewhere.
Ideally, you want that water going outside of your house. In a central air system or a ductless system, the condensation will build up in a drain pan. From the drain pan, the water is emptied outside the house via a condensate drain. In many cases, this is just a simple gravity drain.
A condensate pump is a relatively small, simple device. You install it with the air handler. When the condensate builds up, the condensate pump pumps it out. It uses mechanical force to remove the water, so you don't have to worry about water overflowing the drain pan.
So, if you want to put a ductless mini-split in a location where gravity-fed drainage would be an issue, get a condensate pump. It will keep the water moving out while you stay cool.