Yea, I was confused too. It's important in two ways. One is that EX pokémon normally can't be evolved, so this ability lets Evee EX evolve. You don't normally notice the rule since EX pokémon are typically fully evolved pokémon that can't evolve anyway.
The second part is that you can't typically run more than 2 of the same pokémon in a deck, and pokémon typically only evolve from one type of pokémon. So typically you could not evolve Evee EX into Jolteon, since Evee and Evee EX are two different species of pokémon and Jolteon only evolves from Evee. This ability however lets you do exactly that. Now you can run 2 Evee and 2 Evee EX in the same deck and have all 4 of them evolve into the same Jolteon, Flareon, etc.
Edit: Also, the line "if you play it from your hand onto this Pokémon" means that it won't work with some trainer cards, like those that allow you to pull an evolution card from the deck and play it directly onto the Evee EX.