both terms relate to the roots (such as square root, cube root) of number.
The Index of a root (plural, indices) is the level of a root.
A square root has an index of 2.
A cube root has an index of 3.
A fourth root has an index of 4.
A surd is an irrational root. So, the square root of 4 is two, and is not a surd. But the square root of 2 is approximately 1.41, but cannot be written as a fraction or decimal; it is an irrational square root, so it is a surd. There are also irrational roots with higher indices: The cube root of two is also an irrational number, a surd.
Hope this helps!