Ego depletion refers to the idea that self-control, or 'willpower', is a limited mental resources that can be 'used up' - leaving an individual with limited self-control.

In a state of ego depletion, an individual's impaired ability to self-regulate can be implicated in a wide range of undesirable and maladaptive behaviors, such as acts of aggression."

Source : Wkipedia

The idea was first suggested in 1998, after a set of experiments performed at Case Western Reserve University, US, showed that :

[…] a broad assortment of actions make use of the same resource. Acts of self-control, responsible decision making, and active choice seems to interfere with other such acts that follow soon after. The implication is that some vital resource of the self becomes depleted by such acts of volition."

Source : Journal of Personality and Social Psychology. 74 (5): 1252–1265

Since then, various experimental studies have confirmed the results - while others have refuted them. In addition, the precise psychological mechanisms behind ego depletion are unclear. As are strategies to counteract it.

Some research groups also question the strength of the effect, and others doubt that it's a 'real' effect at all.

While multiple studies provided support for the ego depletion effect, there is currently no direct measure of ego depletion, and studies mainly observe it by measuring how long people persist at a second task after performing a self-control task (the depleting task)
[…]
In 2016, a major study (2141 participants) carried out at two dozen labs across the world using a single protocol failed to find any evidence for ego depletion."

Source : Wikipedia