Given a -dimensional manifold with a metric , a string is a one-dimensional object moving inside . The Nambu-Goto action describes the dynamics of these objects. It’s strongly inspired in the relativistic dynamics of a point particle.
A point particle describes a curve when it’s moving through space and time. Such curve (its trajectory) depends on a single parameter, usually the proper time. Likewise, a string describes a two-dimensional surface called world sheet, and depends on two parameters . Even though the role of both parameters is arbitrary, one can think of as the proper time, and, for any given , would label each one of the points that the string is made of.