Engineering physics is the logical intersection of the fields of engineering and physics. It is a somewhat new discipline, as traditionally physicists and engineers have had little to do with one another.
However, someone noticed that electrical engineering and applied physics had a lot in common. Or maybe the physicists had to call in engineers a lot to build stuff, while the engineers kept having to learn physics so the stuff they built wouldn't break. I don't really know the history. But I do know the curriculum (oh God, do I).
As an undergraduate major, engineering physics is basically a B.S. in physics (physics lab, classical mechanics, electricity and magnetism, quantum mechanics, solid state physics, ), plus the introductory courses required of any undergrad engineer (thermo, programming, statics, chemistry, circuits, and lots of math), plus some additional more advanced engineering courses of the student's choosing. The result of all this is a BSE degree and a big headache. (grin)
The main skill that an engineering physics student possesses is that of problem solving, and the flexibility to work in a variety of fields, something that engineering and physics problems both require.
I am a junior engineering physics major at Case Western Reserve University. I switched to this major after realizing that computer engineering doesn't mean play with computers all day. I had never heard of this before, but the appeal of an engineering degree while taking physics class was not lost upon me.
I spend my days failing to get the grades I deserve, because I'm a slacker, but I am learning a lot of cool things. Check this major out if you think using logic to solve a problem is fun. Stay away if you aren't tops at math, because you have to know crazy math. | 
