It is an intrinsic property of the atom, or rather of the two atomic levels involved in the formation of the line, which determines how much energy a single atom emits or absorbs. There are three quantities commonly used to describe this property, namely oscillator strength, Einstein coefficient and line strength.
The concept of oscillator strength arises from a classical electromagnetic model of the absorption of radiation by an atom. While a detailed understanding of each step in the derivation requires an understanding and recall of some results from classical mechanics and electromagnetic theory, it is not at all difficult to understand qualitatively the meaning of oscillator strength and at least the general gist of the argument that follows.
The proportionality constant is the Einstein coefficient for spontaneous emission for the transition from E2 to E1. It is equivalent to what, in the study of radioactivity, would be called the decay constant, usually given the symbol λ.
For absorption lines (upwards transitions) we can define an Einstein B coefficient such that the rate of upward transitions from level 1 to level 2 is proportional to the product of two things, namely the number of atoms N1 currently in the initial (lower) level and the amount of radiation that is available to excite these upward transitions.