State what is meant by the term 'first ionisation energy' and explain why the first ionisation energy of barium is lower than that of calcium

First ionisation energy is the energy required to remove one mole of electrons from one mole of gaseous atoms, to produce one mole of gaseous ions each with a (+1) charge.

Barium has more energy levels than calcium, and so its outer electrons are further away from the nucleus, and there is more shielding due to inner shells, and so the attraction between the nucleus and outer electrons is weaker than in calcium.