What is meant by the 'First Ionisation Energy' of an element?

The ionisation energy of an element is the energy required to remove the one of the outermost electrons from an atom of the element in its gaseous state. 

 This is quite a difficult process to measure the energy requirements for however, so it is usually scaled up to the energy required or enthalpy change to remove one mole of electrons from one mole of atoms of an element in the gaseous state, which allows us to measure it in J mol^-1 (Energy released per mole). Although, it is much more usual to see kJ mol^-1 used, as working in J mol^-1 means using some unnecessarily large numbers.

The first ionisation energy is the energy requirement for a single electron to be removed from the uncharged elemental electronic configuration (i.e. for lithium this would be 1s² 2s¹) to give a cation with a +1 charge.

This could also be written as a chemical formula: X_(g) -> X⁺_(g) + e^-, where ‘X’ is a particular element.

If another electron was removed from this cation, to give a new cation with a +2 charge, the process would be referred to as the second ionisation energy and so on.

The second ionisation energy could be represented by: X⁺_(g) -> X²⁺_(g) + e^-