Box = Full package, complete with a catchy looking box, drivers, manuals, registration cards, CDs, bundle games. In case of CPUs, you get stock heatsink/fan. In case of video cards, sometimes the clock/RAM speed is faster than OEM. Longer warranty also applies to CPUs.
OEM = Only some of things described above, comes in with maybe a box, or a static bag(in case of hard drives), no heatsink/fan will come with a CPU, in case of video cards, clock/RAM speed can be slower, sometimes some extra features are being taken out. Most of the time it should come with drivers and manuals. Most of the time only 15 day or 1 month warranty for CPUs and video cards. Hard drives however should carry the same warranty.