To tell the computer that you intend to change lanes and aren't unintentionally drifting.
You are, furthermore, required by law to signal lane changes, regardless of if you happen to notice other cars around you or not, at least in every state in the US.
Edit: rereading you comment, you claim to have nearly hit another car when it pulled the wheel, so it sure sounds like you weren't actually correct that there wasn't anyone else around. Please consider that automobiles are heavy machinery, you take on a great deal of responsibility when you get behind the wheel, and that safety code have been written in blood.
At least in my state, ARS 28-754 sb. 1 at the end specifies “if any other traffic would be affected”.
If you aren’t near any other cars, like no other cars in sight, you cannot get in trouble for not signaling if a cop is sitting off the roadway and wants to pull you over for it. Nearly every state has a clause like this.
