Two's complement is the most common way to represent a signed integer using a fixed number of bits.
The high bit can be thought of as the sign bit (though this is arguable, as it represents more than just the sign). If the sign bit is 1, the number is negative. If it is 0, the number is positive or zero. Positive numbers use the standard base-2 representation.
To convert a number N to −N, invert all the bits, then add 1, discarding any carry. This works for any number except the maximally negative number, which has no positive equivalent.
The term two's complement also means the operation described above.