The term ionisation energy refers to the energy required to remove an electron from each atom or ion of an element in a mole of gaseous atoms/ions.
The first ionisation energy is defined as:
'The energy required to remove an electron from each atom in one mole of gaseous atoms. (turning it into an ion with a 1+ charge).'
Sucessive ionisation energies (2nd, 3rd, 4th...) definitions are almost the same except they involve removing an electron from each ion in a gaseous mole of ions. Specifically to produce an ion with the same charge as the number ionisation energy (i.e First ionisatione energy produces a 1+ ion, second produces a 2+, and so on.)