It could be a few things:
First, if your AC Drain Tube is blocked, it can cause water to back up into the system. In your case, moisture may have built up over time from using the AC, and the rain/humidity just pushed it over the edge and backed up into the system. Check underneath for a rubber hose hanging out. Use a compressor and blow air into this - you may be surprised at what comes out: Water, debris, bugs, etc. A quick fix and you'll know right away if this was the cause.
Second, if you've had your windshield replaced, there may be a small gap in the adhesive (This has happened to me.) It may have not presented itself for a while, but heavy rains may expose the issue. If this is the case, water will seep into the gap, run down the inside track of the windshield and can collect in the AC fan/unit. Not always replicated with a hose or during every rain storm, but if the above solution doesn't fix it, look into this as a cause.
Lastly, check the plastic covers/drains under the wipers. These can become clogged and could possibly back up into the system if there's a faulty seal somewhere. Be sure to open the hood and look for other debris in this area.
