Any Pareto efficient allocation is a solution to a planner's problem.
However, the planner is a purely fictional entity; solving the planner's problem requires knowledge of consumers' preferences and all physical resource constraints in the economy.
Thus, a natural question is whether a decentralized market could implement a Pareto efficient allocation, or conversely, whether the outcomes from a decentralized market are Pareto efficient.
The fundamental theorems of welfare economics answer these questions, under certain key assumptions.
The second welfare theorem states that, under certain conditions, any Pareto efficient allocation can be decentralized as a competitive equilibrium.