Ionisation energy is the energy required to remove one mole of electrons from one mole of a vaporised element, to form one mole of unipositively charged ions.
The ionisation energy increases across the period, because the proton number increases. The effective nuclear charge is subsequently larger, so the force of electrostatic attraction between the highest energy electron and the atomic nucleus is greater, so it requires increasingly large amounts of energy to remove this electron across the group.
The ionisation energy decreases down the group, because shielding electron shells exert a dampening effect on the magnitude of electrostatic attraction between the highest energy electrons and the atomic nucleus. So it requires less energy to permanently displace these electrons, and the ionisation energy is subsequently lower.