is an equivalence class of continuous functions from the circle
Two loops are equivalent if they differ by a reparameterization of the circle.
Thus, a free loop, as opposed to a based loop used in the definition of the fundamental group, is a map from the circle to the space without the basepoint-preserving restriction.
Assuming the space is path-connected, free homotopy classes of free loops correspond to conjugacy classes in the fundamental group.
Recently, interest in the space of all free loops
has grown with the advent of string topology, i.e. the study of new algebraic structures on the homology of the free loop space.