what does it mean in math when an x has a circle around it?

Answer 1

I believe it is a bilinear operator

http://en.wikipedia.org/wiki/Bilinear_operator

eg. used in Tensor product

http://en.wikipedia.org/wiki/Tensor_product

Answer 2

Hard to say. What is the context? It could mean a binary operator that's similar to multiplication but defined for a set of object different from the real numbers.

For example, You can define the set of residuals modulo 3. It has 3 elements in it and a definition of multiplication indicated by the x with a circle:
2 (circle x) 2 = 1 because 4 mod 3 = 1

Answer 3

Generally the "x" is the center of the circle.

Answer 4

It depends on your book. Some books call it the tensor product and some call it the direct product.