As the forward reaction proceeds, it will slow down (as the concentration of the reactants decreases) and the backward rate will increase (as those concentrations increase). When the rates are equal, the reaction will appear to have stopped since, at that point, we will be making the products as fast as we are using them, and using reactants as fast as we are producing them.
That is the definition of equilibrium. In a simple sentence:
Equilibrium is when the rate forward and the rate backward are equal.
This idea, that equilibrium can occur with mostly products or with mostly reactants present, is what we really meant when we said that some reactions occur and some don’t. Those we said do occur (and those for which we did stoichiometry problems) were reactions where equilibrium was reached when almost all of the reactants were gone. Those reactions we said didn’t occur were those where equilibrium was reached before a noticeable amount of product was formed.
A Human Example
If this all seems a little weird or hard to grasp, let’s look at a very human example.
The party involves a large crowd that is currently filling a single large room and it is packed enough to feel crowded.
If someone were to open a door to another smaller connected room, people would move into that room.
If someone were to open a door to another smaller connected room, people would move into that room.
But, not everyone would move. If everyone moved into the smaller room that would make things much MORE crowded. Instead, people will move into the smaller room until the “crowded-ness” in the two rooms is about the same. You’ll have lots of people in the big room and a smaller number of people in the small room. Everyone's a little less crowded.
Now there is, of course, nothing that requires people to stay in the room where they are. Some people in the big room will move into the little room. That movement, however, will make the little room more crowded and as a result some people will move out of the little room, back into the big room. The result will be that you will have (roughly) the same number of people in the two rooms that you had before. They may not be the same people, but the numbers will be the same.
If a Fire Marshall were to count heads in the two rooms before and after that move, they would say that nothing had changed, since all they care about is the number of people in the space. We, who know these people at the party, could see that things were changing - that people were moving.
In the same way, when a reaction reaches equilibrium, it appears that the reaction has stopped (the Fire Marshall’s view) when, in fact, things are still moving around and reacting.
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