They take a shower because their skin could dry out. Pool water is chemically treated, and these chemicals leave a residue on the skin which can damage it if not removed.
Also, swimmers in particular sweat quite a bit while racing or practicing. That may be counterintuitive, but its no different than any other heavy exertion sport in that respect. This sweat leaves some residue also, even though the person was immersed in water. A quick rubdown in the shower (usually with soap) eliminates this sweaty residue.
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To wash off the chemicals of the pool water, especially the chlorine which is very drying