Electron affinity (EA) is the energy released from an atom upon the addition of an electron to form the anion. This is defined for atomic species in the gas phase. For example the electron affinity for fluorine is the energy released in the following reaction.
\[{\rm F(g) + e^- \rightarrow F^-(g)} \]
Often electron affinity is treated in a similar way as ionization energy. As such, it is often taught as if it has a similar predictable periodic trend across and down the periodic table. However, electron affinity has essentially no periodic trend. There are particular places on the periodic table where atoms have a finite electron affinty, and others where the EA is zero. These places are where adding another electron will give an atom an electron configuration that is either a filled a shell (or subshell) or half fill a subshell. The largest EA are occur when fillng a shell. Thus the halogen atoms (group 7) have large EA. Fluorine has a large EA (it does go down slightly as you move down the periodic table but Cl is actually bigger than F). Carbon has a reasonalbe EA as adding an elecron would give it a half-filled p subshell. Nitrogen in constrast has no EA since it already has a half filled p-subshell. Likewise the EA of Zn, Cd, Hg are all zero as they have a filled d-subshell. Cu, Ag, and Au are all fairly large as adding one electron will fill the d-subshell. This makes the trend left to right on the periodic table spotty at best. However, elements in the same group (with similar valence configurations) are similar to each other.