There's a sticky at the top of this sub-forum dedicated to this thing. I recommend you spend some time with it: it's good information.
However, in a nutshell:
HPFP = High pressure fuel pump.
It was a problem area on the x35 engines (X3 turbo, 335, 135, 535 models). It tended to fail fairly regularly, usually leaving the owner in a reduced-power "limp mode" engine state.
The very latest versions of these car models seem to have licked the problem. Older versions have been retrofitted with the new fuel pumps, which should mean even they should be relatively problem free now.
Always do right. This will gratify some people and astonish the rest.