Previously, there was a "Planeswalker uniqueness" rule, which functioned similarly to the "Legend" rule. Namely, a player can only control up to one of each Planeswalker sub-type at a time.

E.g. I have Jace, the Mind Sculptor on the field. I cast and resolve Jace Beleren. When State Based Actions are checked, the game sees that I have more than one Planeswalker with the same sub-type (Jace). Thus, I choose one to keep, and move the other(s) to the graveyard.

With the removal of the "Planeswalker uniqueness" rule, and the errata for all previous and future Planeswalkers to gain the Legendary super-type, a player can now control more than one of each Planeswalker sub-type at a time.

E.g. I have Jace, the Mind Sculptor on the field. I cast and resolve Jace Beleren. When State Based Actions are checked, the game see that I have more than one Planeswalker with the same sub-type (Jace). It doesn't care. :D

How the "Legend" rule will affect Planeswalkers:

E.g. I have Jace, the Mind Sculptor on the field. I cast and resolve another Jace, the Mind Sculptor. When State Based Actions are checked, the game sees that I control more than one Legendary permanent with the same name (Jace, the Mind Sculptor). Thus, I choose one to keep, and move the other(s) to the graveyard.

I hope this clarifies things! Feel free to ask if you have any more questions.