Consumer equilibrium refers to a situation in which a consumer has allocated their resources in the perfect possible way. They have spent their resources in such a way that there is nothing that they could possibly do to get themselves any more utility.
As consumers, we have limited resources. We have to decide what to spend those resources on. We have to budget our time and our money. When we do so, we have to make choices between buying various things. We might have to decide, for example, whether to spend money on going to a movie or on buying music online. More likely, we have to decide how much money to allocate to each of these.
Consumer equilibrium occurs when we have made this budget in the best possible way given our own tastes. We have gotten the greatest possible utility out of our resources. What this means in terms of our example is that going to see one less movie and buying music instead will not increase our satisfaction. We have achieved a perfect balance between movies and music.
Consumer equilibrium, then, occurs when we have budgeted our resources in exactly the right way and we can get no marginal utility from making any changes.