When we refer to constant pressure like in Charles law what is this pressure? The pressure of the gas or the pressure that the container (the piston maybe) exert on the gas? Also does atmospheric pressure is taking into account when we refer to constant pressure?
It is all three things you mentioned. It is the force per unit area that the gas exerts on the wall of the container, the force per unit area that the wall exerts on the gas, and the force per unit area that each parcel of gas exerts on its neighboring parcels (and that they exert on it). If the container is totally isolated from the atmosphere, the atmospheric pressure is irrelevant to the gas pressure inside the container.