You and Sam have already given hints toward what I normally provide as a 'wordy' description of Fatou's Lemma, but not written it explicitly.
To answer the question, I suggest you use: "Energy can not be gained through relaxation".
I keep in mind the standard example where $ f_n(x) = \begin{cases}n,\text{ for }x\in[-1/(2n),1/(2n)]\\ 0,\text{ otherwise}, \end{cases} $ where $x\in\mathbb{R}$ and we use standard Lebesgue measure on $\mathbb{R}$. Then the measure of each $f_n$ is 1 for every $n$, i.e. each element of the sequence has unit energy, but $f_n$ converges uniformly to the zero function (I say "$f$ relaxes to zero"), which has measure zero, and so zero energy.
The example proves the obvious statement that "Energy can be lost through relaxation". It also begs the question of whether or not one may gain energy through relaxation.
Fatou's Lemma gives the non-trivial answer: "Energy can not be gained through relaxation".
Caveat: It is not always appropriate to think of limits of functions as a 'relaxation'. Plenty of things can blow up in a limit (the derivative of a smooth approximation of a discontinuous function must blow up for example). Still, I find it to fit here very well.