The best way to understand the stack is to actually "stack" cards as you cast them.
I cast a creature spell. It goes down on the table.
In response, my opponent casts Essence Scatter, placing it on top of my creature.
In response, I cast Dissipate, placing it on top of Essence Scatter.
In response, he casts Dispel, placing it on top of Dissipate.
Both of us pass priority (i.e. neither of us make any further responses). Once this happen, the cards on the stack resolve from top to bottom. Dispel goes off, countering Dissipate. Since Dissipate has now been countered, Essence Scatter goes off. Since Essence Scatter went off, my creature is now countered and goes to the graveyard.
In short: The stack is the chain of spells responding to other spells, and the spells resolve in a "first on, last off" order.
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