The Federal Aviation Administration (FAA) is the agency within the Department of Transportation responsible for the safety and regulation of all civil aviation in the United States. The FAA writes the regulations (the Federal Aviation Regulations, codified in Title 14 of the Code of Federal Regulations), certificates pilots and aircraft, and manages the airspace.
The NAS is the network of air navigation facilities, airports, airspace, rules, and personnel that allows aircraft to operate safely. As a remote pilot you are now a participant in this shared system, even though you operate from the ground. The core principle is the same one manned pilots follow: see and avoid — for you, that means keep your aircraft in sight and yield right-of-way to all other aircraft.
Under 14 CFR 107.37, a small unmanned aircraft must always yield the right-of-way to all other aircraft, manned or unmanned. You may never operate so close to another aircraft as to create a collision hazard. A drone has no passengers and is replaceable; a manned aircraft is not. This asymmetry drives nearly every operating limitation in Part 107.