The Eulerian equations watch the fluid move thru a mesh which stands still. The dynamic variables at a point in the mesh are density, temperature, fluid velocity. Static information for the mesh point is the geometric details. Often the mesh is layer out in a rectangular fashion which eliminates per mesh point information.
For the Lagrangian equations the mesh moves with the fluid and the dynamic variables are temperature, the positions and velocities of the mesh point. Each mesh point has an associated constant mass.