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Consumer equilibrium is where the consumer's Budget Line just touches at a tangent the highest of the Indifference Curves between two products. THis is the analytical approach, see the graph below ( I will add this later today). wmw
WWENDT has already (and correctly) replied to your question - I'll just restate the answer in non-technical terms. Consumer equilibrium is simply the point at which a consumer is able to purchase a basket of goods by exhausting her wallet. She can't spend any more than she would at consumer equilibrium, and she is indifferent to any other basket of goods that is available to her at her spending capacity.
When consumers make choices about the quantity of goods and services to consume, it is presumed that their objective is to maximize total utility. In maximizing total utility, the consumer faces a number of problems, the most important of which are the consumer's income and the prices of the goods and services that the consumer wishes to consume. The consumer's effort to maximize total utility which helps them in taking decision about how much the consumer will consume of a number of goods and services, is referred to as consumer equilibrium.