You import an EPS that should have a transparent background, but when you print it, the background is white.
By default, Frame sets the background (or fill, really) to white for all EPS files. In most cases you merely need to select the graphic and set its fill to none.
Occasionally you may encounter an EPS that doesn't seem to change. (Personally, I found this once in a while in Frame 5, but not yet in Frame 6.) When you cannot override this in Frame, you can change it in the MIF. In summary, imported EPSs have a MIF parameter called <Fill n> you need to change. Its default is 7; you need to change it to 15.
Note that I usually just do a replace on the whole file because I find that a background either needs to be changed, or if it doesn't need it and it's changed anyway, then I don't care.
Also, note that on the screen, the EPSs still appear white. They will be okay when printed or made into a PDF.
Credits to a Mark Barratt. I have no idea who Mark is; I just read his name on the Adobe forum.