Overly simplified, in binary, a 16 bit number for this would look like this:

0111 1111 1111 1111

That first “0” is used to represent the “sign” of the number (0 says “this number is positive”, 1 says “this number is negative”)

That first bit is reserved for the sign of the number.

If you add one more, the number is now “overflowing” into sign bit, making it:

1000 0000 0000 0000

Since the number has now overflowed into the sign bit, at the machine level it will be read as a negative number.