Yes - it is normal. As the air passes across the coils - the humidity es extracted as condensation and drips into a pan, then it is either diverted outside or into the plumbing drains.

You will want to purchase some chlorine tablets and put them in your AC drain pan periodically (I do it every few months or whatever the bottle says) to ensure that they are kept clean. In the Winter, when the heat is running - it will be dry.