Veteran Rank also 'replaces' XP when high enough in level, with increases granting more stats and access to better gear. Skill points are still earned when levelling up veterancy.
The studio also confirms something we'd all expect to be present: "...yes, you can have multiple characters." The full 'Ask Us Anything' is available via the official website.
"Veteran Points are similar to XP, and your Veteran Rank goes up as you gain them (like gaining a level). You’ll get Veteran Points for accomplishing certain tasks in the game," explained Zenimax. "Imagine you were told you needed to kill a specific NPC or monster in a dungeon. If you’re level 50, you’ll get Veteran Points for accomplishing that goal."
"When you get enough Veteran Points, you go up in Veteran Rank. There will be lots of ways to gain VP. You could gain Veteran Points in PvP or in Adventure Zones." The TESO team is yet to fully disclose the Veteran Rank system.
"VRs do improve your character’s power by granting stats and the ability to equip better gear, though the increases are smaller than the ones you’ll gain through normal leveling. This will make it easier for you to visit wherever you want in the next alliance you play, and will make it easier when you’re grouping with friends who may not be as advanced as you are."
"You’ll continue to gain skill points while increasing your Veteran Ranks, so it’s really a time when you’ll be able to broaden your character’s skills. We’ll release a full write-up for VPs and VRs in the near future."