I cannot speak for all branches as they are all different (but mostly similar), but I can speak for the Army as a 4yr HPSP student graduating next year. Basically, the Army has needs, but so do you. It is important to realize this before you start.
(All of the following numbers and specialities are for demonstration purposes and are not to scale!)
For example, the Army projects a need for 20 new surgeons in 5 years. There is the capacity in the Army to train all 20 of these surgeons (sufficient residency spaces). Also, for example, say there are 50 students who want to train in surgery. Up to this point it's pretty similar to the civilian match except on a smaller (and potentially, more competitive) scale. The difference is where do the remaining 30 students go. This is why you must choose 5 programs (see the post in this forum for more details) for the Army match. Say for example there are only 4 programs for surgery in the Army (I don't recall the actual number, remember this is for demonstration only). Your best bet would be to rank those 4 programs as your top choices (and interview at each spot), but then you must choose something else for number 5. Most rational people would choose a transitional program and then reapply after finishing that (that's another entire post in and of itself).
The story is different in the specialities that the Army does not have the capacity to sufficiently train all the physicians for its needs (Orthopedic surgery is one such specialty). In this case the Army will give out deferrments for training at civilian programs (but the Army's needs still apply and the number of deferments + the number of Army-trained residents is decided by the Army's projected need).
That being said, the real question is "How many people get one of their top choices?" For the Army the figure tossed around is usually 85% of students get either their first or second choice. Therefore it is really not all that different than the regular match, just for the most part, consider the military programs to be the more competitive and do well in school. You will succeed.
2Lt GeoLeoX
ps. as I am currently in the middle of ERAS and the Army match application, feel free to ask me any questions about it.