There can be many nearby Pokémon in the list but one of them show before other in the right bottom corner without clicking on it and it's mostly one of the unlocked one. So is there any significance of changing it?
By selecting one of the "nearby" pokémon, it allows you to track your distance from that pokémon without keeping the "nearby" list open.
For instance, if I wanted to track an Eevee, I can't tell how far away it is if I don't have it selected, or if the "nearby" menu isn't open:
However, if it is selected, I can see my distance from that pokémon in the bottom right corner, making tracking it while walking around much easier: