We know more universally, any particle or event trace in worldline, and what it takes is the least/stationary action path. In string theory, the particle/event is replaced by string and trace trajectory that is one-dimensional is replaced by a two-dimensional surface. And the worldline is recalled the worldsheet.

Taking the typical mathematical thinking approach, instead of tracing in one-dimension using one parameter lambda, we introduce an additional parameter sigma and try to figure out the surface area in three-dimensions from two-dimension parameters:

h is the metric also here, and for one-dimensional higher measurement.

the purpose is to find the equation for string’s least action trajectory – worldsheet.