On most modern computers this means 65,536 bytes (8 bits) of random access memory, which can be both read and written.
On older computers this could mean a variety of different things depending on the architecture of the specific computer, some are:
- 65,536 words of random access memory, which can be both read and written. A word could be any number of bits in length, with values from 12 bits to 60 bits being most common. No entity smaller than a full word is directly addressable on these machines.
- 64,000 words of random access memory, which can be both read and written. A word could be any number of decimal digits in length, with values from 5 decimal digits to 12 decimal digits being most common. No entity smaller than a full word is directly addressable on these machines.
- 65,536 characters of random access memory, which can be both read and written. A character was typically 6 bits in length.
- 64,000 characters of random access memory, which can be both read and written. A character was typically 6 bits in length.
- 65,536 bits of random access memory, which can be both read and written. Any individual bit or group of bits (of any length up to 65,536 bits) is directly addressable on these machines.
- etc.
One really needs to be more specific with units to be unambiguous.