The topological circle is a compact, connected topological space. It is a 1-dimensional smooth manifold (indeed, it is the only 1-dimensional compact, connected smooth manifold). It is not simply connected.
The circle is a model for the classifying space for the abelian group Z, the integers. Equivalently, the circle is the Eilenberg-Mac Lane space K(Z,1). Explicitly, the first homotopy group π1(S1) is the integers Z. But the higher homotopy groups πn(S1)≃*, n>1 all vanish (and so is a homotopy 1-type). This can be deduced from the result that the loop space ΩS1 of the circle is the group Z of integers and that S1 is path-connected.