degrees of freedom
The number of independent ways a molecule can move or store energy: sliding along the x, y, and z directions, spinning about its axes, or vibrating along a bond. Count them up and you know how the molecule holds thermal energy.
Precisely, translational motion gives every molecule 3 degrees of freedom (x, y, z). A linear or diatomic molecule adds 2 rotational ones, since it can spin about two axes; classically, spinning about the bond axis itself does not count. Each vibrational mode adds 2 more (kinetic plus potential). By the equipartition theorem each degree of freedom contributes (1/2) k_B T.
Use: the total number of degrees of freedom f sets the internal energy U = (f/2) n R T and the molar heat capacity at constant volume C_V = (f/2) R. A monatomic gas has f = 3, giving C_V = (3/2)R; a diatomic gas at room temperature has f = 5, giving (5/2)R.
A monatomic gas such as helium has 3 degrees of freedom; a diatomic gas such as nitrogen has 5 at room temperature.
The count of independent ways a molecule stores energy.
Which degrees of freedom are active depends on temperature: vibrational modes stay frozen out until the gas is quite hot, which is why the count and the heat capacity change with temperature.