In order to assign a string to b, you have to move it or copy it from where it was. You can't move it out of a, because that would be unsafe -- the string owned by b would then be pointing to somewhere inside a. So, your only option is to copy it out. Because String is non-Copy, you would have to clone it:
b = a[index as usize].clone();
By the way, a more idiomatic way to write that loop would be
for b in a {
// do whatever with b
}
Or, if you still want access to the index,
for i in 0..a.len() {
b = a[i].clone();
}