Simple: one can contain negative values, the other can't.
To expand a little, a signed value uses one bit (usually the top, or most significant bit) to indicate if the number is positive or negative, and an unsigned integer uses all available bits for the number - so the number of different values that can be held is the same, but the range of values is different.
Assume we used a 4 bit processor (to make the numbers easier)
Unsigned:
Bits Value (decimal)
0000 0
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 8
1001 9
1010 10
1011 11
1100 12
1101 13
1110 14
1111 15
Signed:
Bits Value (decimal)
0000 0
0001 1
0010 2
0011 3
0100 4
0101 5
0110 6
0111 7
1000 -8
1001 -7
1010 -6
1011 -5
1100 -4
1101 -3
1110 -2
1111 -1
-8 in this scheme is sometimes treated as "minus zero" but you can probably ignore that!