Enthalpy vs ∆Enthalpy
We know that enthalpy represents the energy of a system. So, now think about it? Measuring the energy of a system? Consider all the changes and influences a system is under. This makes it really difficult (we could say impossible) to calculate the enthalpy of a system.
But we do know one thing, that the enthalpy depends on two factors.
A system will experience change in enthalpy if it's internal energy is changed and/or if work is done on/by it.
So what we do is that we assume an initial state where we start our observation and a final state where our observation concludes. And the changes in state cause particular changes in enthalpy and this change in enthalpy of the system is what matters to us anyway.
Why did we define it then if we don't use it?
We just know that a particular quantity depends on two particular factors. It's just that we understand the fact that it is meaningless to calculate the enthalpy of a system - because we do not know where to start from? Where will you start from? You need a point where the enthalpy was zero initially and then gained enthalpy right? But imagine - doesn't that mean there won't be any atomic activity at all if we're starting from zero enthalpy? And if there wasn't atomic activity then that chemical specie might not even be able to exist? It's complicated.
But then we realise: all that matters to us is just change in enthalpy during a thermodynamic process. And that is what thermodynamics is essentially all about - energy in motion. Thermodynamics is but a study of states (this was mentioned in NCERT Chemistry). So we study the change in Enthalpy from one state to another.
We define the enthalpy and what it depends on so that we can observe the factors that it depends on.