the | is more bitwise operation.
they clear the lower 4 bits of PORTB, then use the 'or' to set them equal to first the upper 4 bits of the data (c>>4) and then do it again for the lower 4 bits, with a strobe after each one.
the PORTA*8+2 crap at the top looks like PICC's way of defining a bit variable mapped to a certain bit in a certain register. it takes the address of PORTA (&PORTA) and multiplies it by 8 (8 bits per byte) and then adds 2... therefore if PORTA were at address 100, it would be the 802nd bit you were looking at. yes, it's an odd way of doing it, but i've seen it used in other compilers... (although it's usually not the preferred method because it's rather obscure)
for the strobing, well, that's basically what they're doing... if this is sample code for PICC, most likely that happened to be a more efficient way of doing it. toggling PORTA bit 3 with boolean operators would be much more intuitive and you could do it that way instead.