To tackle this question, we need to understand the concept of electron gain enthalpy.

Electron Gain Enthalpy: Electron gain enthalpy is defined as the energy change that occurs when an electron is added to an isolated gaseous atom. This process can either result in energy being released or absorbed, depending on the nature of the atom. For most atoms, incorporating an additional electron releases energy, which implies a negative enthalpy change.

Now, let's analyze the given options:

1. Energy released when atoms combine to form stable molecules: This statement refers to bond formation and is not related to the addition of an electron to a gaseous atom. Hence, this is incorrect.
2. Energy released or absorbed when isolated gaseous atom gains electron: This statement accurately defines electron gain enthalpy. Therefore, this is the correct choice.
3. Energy required to remove electron from isolated gaseous atom completely: This describes ionization energy, not electron gain enthalpy. Hence, this is incorrect.
4. Energy required to break bonds present in chemical compounds: This refers to bond dissociation enthalpy, which is unrelated to electron addition. Hence, this is incorrect.

Therefore, the correct answer is: 'Energy released or absorbed when isolated gaseous atom gains electron' as it precisely defines electron gain enthalpy.