I couldn't find any explanation inside the game. Maybe it's the number of the turns passed since the beginning of the current combat?
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3It takes roughly two tries to understand how they work. Second try is when you have 0 energy. – user135338 Apr 26 '19 at 14:03
The answer is:
Some cards can have X Energy cost. These cards consume all of your remaining Energy upon use, and their effect varies with how much Energy was consumed.