The previous post hits it pretty close. Level of trauma centers is a designation by the American College of Surgeons that is based primairly on the avalibility of staff and speclities 24//7/365.
The easiest way to think of it is that a Level I trauma center can handle anything and everything that is sent to it via the Emergency Department. There will be no pack and ship to a higher care facility.
Nuts and bolts wise, there are 'criteria' that determine the level of a trauma as it rolls to the doors of the local Emergency Department. If its a small town and whatever coming is 'really bad' then the patient will be stabilized and sent to the higher care facility (usually a Level I trauma center). This facility will have a large team at the doors waiting as a patient rolls in.
The team consits of: Trauma Surgery Attending, Anesthiology Attending, Emergency Medincine Attending, all the aboves line of residents and medical students if they are on the service, respiratory techs, several nurses trained in emergency care... also there will be an Operating Room that is avalible with full staff (scrub techs and the such) at any time of the night/day/year, full CT capabilites with radiology to read 24/7, there will be certain specialists avalible withing a given time frame, such as neurosurgeons, vascular surgery, orthopaedics, etc....and some of the sidelines to this is active trauma research as well as a certain volume of patients that met the criteria.
The exact critera to make a trauma 'activated' (i.e. pagers set off on all the above mentioned people to be in the Emergency Department NOW) varies slightly from hospital to hospital... but generally: Motor vehicle crash over 45mph, prolonged vehicle extraction, fall over 8 feet, burns greater than 20%, traumatic amputation... some even include any field intubations, any gun shot wound, knife wound usually to the chest or abdoman.
Level II and III vary in that they do not have as much avalible as the above. I think Level II is the typical 'large' place without residents as most surgical attendings are at home overnight and instead of requiring to be at the patient in 10 mins or less they have like an hour. Also, a Level I trauma center may get a trauma that they rank a Level II which would mean not as many of the above would need to come to the Emergency Department. Criteria is similar to above but just a little less... maybe burns to 10-20%, fall from 4 feet, MVC reported with an unstable patient, blunt injury to abd but patient stable, etc...
Hopefully my ramblings made sense and shed some light to your question. I think the first time you see an 'activated trauma' will be a memorable experience. I still remember my very first and was simply amazed at everyone doing their part as a team. I am not very happy to be a member of that team....