What does the 2 arrow icon mean?

Original answer:

For these Pokemon you have an extra button under their profile. Exchange. It shows a "Tree View". Which I'm still not sure what it does, but this is what the arrows mean, that you have access to their "tree view". I'm guessing that having all the Monsters on the tree allows you to upgrade/combine/evolve them to the one on the top of this tree.

I'm editing the answer now that I know exactly what the arrows mean.

Detail answer:

The arrows mean that these Specific Pokemon and Elemental attribute are part of an available Exchange. You can click on the Exchange icon in the Pokemon info and you will see the Tree it belongs to. After leveling up your account, not your Pokemon, you get access to an Exchange building. In this building you can exchange the Required Pokemon for another. Exchanges are done 4 Pokemon at a time, you can see the Exchange Tree divided in 4 smaller Exchanges, I call them lower level Exchanges. These require 4 Level 30, 4 Star Specific Pokemon and Elemental attribute.

Have in mind that the Tree shows you the Evolved Pokemon, but when you go on the Exchange Building, you get the Non-Evolved Pokemon at Level 1, and 4 or 5 Star, depending the Exchange that you completed. Lower level Exchange costs 100,000 and Higher level Exchange costs 500,000.