Do offsets in assembly represent addresses or bits?

I am a bit confused, will inc [esi + 8] (lets say [esi] points to 0x0000001F in 8-bit memory) increment 0x00000027 or will it affect 0x00000020? I have seen a video implying it will affect the latter whereas regular pointers in ram go by addresses, not bits.

Addresses are bytes. This will increment 0x00000027.

This doesn't assemble because you're missing the size though. inc {byte|word|dword|qword} ptr [esi + 8] is what you want. (Operand size is required)