Here's why:

* Degrees of freedom represent the number of independent ways a system can move.

* A surface restricts the particle's movement to a two-dimensional space.

* The particle can move freely in two directions along the surface, but it cannot move perpendicular to the surface.

Think of it like this:

* A bug crawling on a table can move forward, backward, left, or right. It can't fly up or burrow down.

* A ball rolling on a sphere can move along the longitude lines and latitude lines of the sphere. It can't move in or out of the sphere's surface.

Therefore, the particle has two degrees of freedom, representing its ability to move in the two independent directions along the surface.