I'm going to assume that this is an intake air sensor. It actually takes a reading of the temperature of the air entering your engine by means of electrical resistance or somesuch method.

Now, if you disconnect this you're getting error codes, and well...thats not a good idea. If you just leave this sitting there, provided that it doesn't fall against your exhaust manifold and melt or something, its going to read some HOT ass air when you're really getting cold air. Due to this reading of hot, your engine is going to attempt to adjust your fuel flow to achieve a stoichometric mixture. While its doing this, the gasses exiting your engine (which is now running lean because less fuel gets dumped for hotter air) will blow by your O2 sensor(s). These sensors are going to read the lean mixture and prompt your engine to try to enrich the mixture to achieve a perfect mixture. Now, in the end what will happen? I'm a simple car junkie, I'm not sure which sensor has bigger balls, but the ensuing fight won't be pleasent for your car's computer or performance. Your car will pretty much run like a dirty asshole in my prediction.

Bottom line, if you've got sensors, best to leave them attached and working properly.