What is the difference between signed and unsigned variables?

Signed variables, such as signed integers will allow you to represent numbers both in the positive and negative ranges.

Unsigned variables, such as unsigned integers, will only allow you to represent numbers in the positive and zero.

Unsigned and signed variables of the same type (such as int and byte) both have the same range (range of 65,536 and 256 numbers, respectively), but unsigned can represent a larger magnitude number than the corresponding signed variable.

For example, an unsigned byte can represent values from 0 to 255, while signed byte can represent -128 to 127.

Wikipedia page on Signed number representations explains the difference in the representation at the bit level, and the Integer (computer science) page provides a table of ranges for each signed/unsigned integer type.

Signed variables use one bit to flag whether they are positive or negative. Unsigned variables don't have this bit, so they can store larger numbers in the same space, but only nonnegative numbers, e.g. 0 and higher.

For more: Unsigned and Signed Integers

Unsigned variables can only be positive numbers, because they lack the ability to indicate that they are negative.

This ability is called the 'sign' or 'signing bit'.

A side effect is that without a signing bit, they have one more bit that can be used to represent the number, doubling the maximum number it can represent.

Signed variables can be 0, positive or negative.

Unsigned variables can be 0 or positive.

Unsigned variables are used sometimes because more bits can be used to represent the actual value. Giving you a larger range. Also you can ensure that a negative value won't be passed to your function for example.

Unsigned variables are variables which are internally represented without a mathematical sign (plus or minus) can store 'zero' or positive values only. Let us say the unsigned variable is n bits in size, then it can represent 2^n (2 power n) values - 0 through (2^n -1). A signed variable on the other hand, 'loses' one bit for representing the sign, so it can store values from -(2^(n-1) -1) through (2^(n-1)) including zero. Thus, a signed variable can store positive values, negative values and zero.

P.S.:
Internally, the mathematical sign may be represented in one's complement form, two's complement form or with a sign bit (eg: 0 -> +, 1-> -)
All these methods effectively divide the range of representable values in n bits (2^n) into three parts, positive, negative and zero.

This is just my two cents worth.

I hope this helps.