My basement drain has been clogged for at least 1-2 weeks. Went downstairs and noticed that the water has drained. It was a pretty big clog. How could it fix itself without being snaked or having a plubmber come fix it.

Your blockage built up head pressure behind it. When the pressure reachede a certain point it started the clog to move. Once it broke free the water flushed it out into the main. Did that answer your question? Cheers, Tom

Now would be a great time to dump several buckets of not water down that drain. This would help break up and/or move the clog out to the city line.