A topological space
is said to be simply connected if it is path connected
, and if any loop
is the space is homotopic
to a constant
Pictorally, you can think of a loop in a space as being like noose wrapped around part of the space; if the space is simply connected, you can always be sure that you can pull the noose down to nothing.
For instance, the surface of a doughnut (called a torus) is not simply connected, while the surface of a sphere is.
An equivalent formulation is that a space is simply connected if and only if its fundamental group is trivial.