for example, Fast recovery diode can block voltage up to 6 kV and is able to block current up to 1.1 kA.. what voltage does it block? is it forward voltage? or PIV? or else? and how does it block voltage or current?
It block 6KV, means PIV could be 6KV or higher, it is not forward bias voltage, and is blocked due to increased depletion region, due to reversed bias....an 1.1KA forward bias current could be blocked.
Conduction is forward current pulse rating of 1.1kA, where that V can be computed from Vk+ I* ESR of bulk resistance ESR, due to Pd rating approximately ESR ~ 1/(k * Pd) [Ohms] from my experience. k = 0.5~1 depending on device size. Vk is the knee of the diode VI curve where it becomes linear.
Blocking is just leakage current at PIV (reverse) rating of 6kV Max.
6kV is the peak inverse voltage (P.I.V).. while reverse bias. Practically, if any reverse voltage (probably negative surge 6kV) charge your diode, it will be okay. And, 1.1 kA is the acceptable current rating on forward bias. It can be nominal rms current or d.c forward current. So, if any forward current flow with value 1.1kA (rms) or 1.1 kA (d.c) trough your diode, it will be safe.
here i attach a sample datasheet with information that you need. hope this may answer your question. :)