Why enthalpy increases when we heat a gas at constant volume

Not all increases in enthalpy are associated with $pv$ work. A simple example is the increase in enthalpy of a substance undergoing a phase change from a solid to a liquid at constant pressure and temperature. In this case there is heat transfer and no $pv$ work being done. The increase in enthalpy is called the latent heat of fusion.

Given a closed system and a constant volume process involving a gas we have

$$Delta H=Delta U+VDelta p$$

$$Delta U = Q-W=Q-int pdV$$

For a constant volume process $dV=0$ and $Q=mC_{v}Delta T$, therefore

$$Delta H=mC_{v}Delta T+VDelta p$$

I just want to know if there is a analogy, means what is the physical meaning of enthalpy

Enthalpy is not a fundamental property in thermodynamics, like internal energy, entropy, pressure, volume and temperature. It is a property derived from other properties, namely internal energy, pressure and volume.

Returning to your original equation

$$Delta H=Delta U+VDelta p$$

For an open system $VDelta p$ is referred to as flow work, the work involved in moving mass into and out of an open system where there is a difference in pressure that must either be overcome or that aides in moving mass into or out of the control volume. So for an open system, the utility of $H$ is that it encompasses both the change in internal energy and the flow work, into one thermodynamic property called enthalpy.

Hope this helps.