Perfect competition is an economic model that describes a hypothetical market form in which no producer or consumer has the market power to influence prices. According to the standard economical definition of efficiency (Pareto efficiency), perfect competition would lead to a completely efficient outcome. The analysis of perfectly competitive markets provides the foundation of the theory of supply and demand.
To be exhaustive, note that some economists do not agree with this presentation of the model of perfect competition. Many reasons are advanced, but one of the main is that it focuses on unnecessary conditions (atomicity, perfect information...) while it does not allow an answer to the question : "If agents are price-takers, who sets the prices ?" Indeed, in this model, as firms and consumers can not set the prices, it can't be—as it is often said (e.g. below)—that it is the firms who fix them. So, actually, there is a need for a benevolent agent who proposes prices to firms and consumers and fixes the ones at which exchange will occur. They also think that the argument that a global entity called "the market" could fix the prices, when its constituents (producer...