A great deal of the suspense in Endgame comes from Hamm and Clov's constant arguing. Clov repeatedly says that he will leave Hamm, but proves unable to do so. Hamm mistreats him, and in the middle of the play, we learn that Clov has probably been Hamm's servant since childhood. At two different points, Clov questions Hamm's authority.
The first time:
Do this, do that, and I do it. I never refuse. Why?
You're not able to. (1.454-455)
And the second:
There's one thing I'll never understand. (He gets down.) Why I always obey you. Can you explain that to me?
No…Perhaps it's compassion.
(Pause.) A kind of great compassion. (1.745-746)
In Endgame, the master-servant relationship is given center stage. The play, which is always on the brink of ending, is prolonged by the different ways that Hamm manipulates Clov and gets him to obey him. Without this master-servant relationship, the play would come to a halt (because Clov would bolt).
A lot of people like to talk about how Beckett put a "state of mind" on the stage with his breakthrough play Waiting for Godot. No one had ever depicted "waiting" before. Now, if Beckett is putting a state of mind on the stage in Endgame, then what does that state of mind look like? We're going to pull in a bit of terminology from the good doctor Sigmund Freud to explain it.
One of the ways that Freud modeled the mind was with the concept of the superego, the ego, and the id. Beckett was very familiar with this concept. The id consists of our base animal desires, and the superego is a bit like our conscience. Our superego is what tells us to act one way or another, to restrict our behavior in a certain way, but it is also the thing that always tells us that we are not good enough. The superego is the "boss." That leaves the ego, which is basically what we think of as ourselves. The ego is caught between the base desires of the id, and the bossiness of the superego. It is like a servant with two masters.
Enter Endgame. It's not too difficult to read Hamm as the superego. Hamm is, for example, the most complex thinker and the one that asks that they all pray to God. Then we can read Nagg as the id. In his very first line, Nagg cries, "Me pap!" (1.76) Throughout most of the play, he doesn't want much more than candy, attention, scratches, and kisses. That leaves Clov as the ego, the exhausted servant caught in between two masters: the ego and the id, instinct and idealism. He thinks to himself, "When I fall I'll weep for happiness" (1.794).
Read this way, Endgame captures the interplay between the different parts of our minds, our cravings and our self-demands. Clov is our desperate attempt to keep everyone happy, to maintain balance and order. As he says, "I love order. It's my dream. A world where all would be silent and still and each thing in its last place, under the last dust" (1.569).