When a block of mass $M$ is suspended by a long wire of length $L$, the length of the wire becomes $(L+l)$. The elastic potential energy stored in the extended wire is:

The work done by the stretching force is stored as elastic potential energy ($U$) in the wire.For a wire stretched by an extension $l$ under a force $F$, the potential energy is:
$$U=\frac{1}{2}\times \text{Force}\times \text{Extension}$$
Here, the force exerted by the block is its weight, $F=Mg$.The extension is $l$.Substituting the values:
$$U=\frac{1}{2}Mgl$$