Lagrangian and Hamiltonian. What are these in layman terms?

[avito009]

All I know is that Lagrangian is kinetic energy- potential energy and Hamiltonian is kinetic energy + Potential energy.

Why do we calculate the lagrangian or hamiltonian?

 

[avito009]

When the Lagrangian is maximised it gives equations of motion.

 

[Orodruin]

Why do we calculate the lagrangian or hamiltonian?

Why do we do anything in physics? We do it because it gives a good description of what we can observe.

When the Lagrangian is maximised it gives equations of motion.

No, when the action is extremised (i.e., maximised, minimised, or finding a saddle point) we find the equations of motion. The action is the time integral of the Lagrangian.