It's a slightly confusing one 
32 bit is referring to 32 binary numbers (i.e only 0's and 1's) being the largest number these systems were designed to handle.
It's why there's a 4GB limit on 32 bit systems, because 11111111111111111111111111111111 in binary = 4,294,967,295 in decimal.
There's 1024 bytes in a kilobyte, 1024 kilobytes in a megabyte, etc.
So 4GB x 1024 (MB) x 1024 (KB) x 1024 (B) = 4,294,967,296. That's one number higher than we can write with only 32 binary bits!
So someone decided hey, instead of creating architecture that only supports 32 binary numbers in a row, lets make one that supports 64 in a row. Now we can store much larger numbers.
Unfortunately, when AMD invented that new 64 bit architecture, they infuriatingly decided to call it "AMD64". But companies like Intel also use this architecture, so the name is now stupidly misleading as it seems you'd only choose an "amd64" build if you had an AMD cpu.
For that reason, lots of people call it "x86_64" or just "x64" these days.
32 bit is referring to 32 binary numbers (i.e only 0's and 1's) being the largest number these systems were designed to handle.
It's why there's a 4GB limit on 32 bit systems, because 11111111111111111111111111111111 in binary = 4,294,967,295 in decimal.
There's 1024 bytes in a kilobyte, 1024 kilobytes in a megabyte, etc.
So 4GB x 1024 (MB) x 1024 (KB) x 1024 (B) = 4,294,967,296. That's one number higher than we can write with only 32 binary bits!
So someone decided hey, instead of creating architecture that only supports 32 binary numbers in a row, lets make one that supports 64 in a row. Now we can store much larger numbers.
Unfortunately, when AMD invented that new 64 bit architecture, they infuriatingly decided to call it "AMD64". But companies like Intel also use this architecture, so the name is now stupidly misleading as it seems you'd only choose an "amd64" build if you had an AMD cpu.
For that reason, lots of people call it "x86_64" or just "x64" these days.
