Real mode, on the 80286 and later members of the Intel x86 line, refers to a mode of the CPU in which the extended architectures of the later chips, including hardware support for virtual memory, is not enabled.
These chips power on in real mode, in which they appear to be 8086's; this is for purposes of backward compatibility at the object code level. A small extension to that architecture allows them to switch into protected mode, where all the extended features of the later architectures are available.
Real mode in the later x86 machines is almost entirely the same as the 8086, but there are minor differences (e.g. different Instruction Clock Counts).