There is a pretty good description right on the play settings screen in the preview.
A good analogy is that recital mode is a lot like the way most other rhythm games play all the time: straight-through at a fixed speed. The only control you really have is pause/resume. This is basically to level the playing field and make it a little more sane for me to try and find a way to score people uniformly so the results can go on the upcoming online scoreboard.
The existing modes: melody practice (formerly "practice") and rhythm practice (formerly "rhythm") keep scores locally on local scoreboards with no names or identifiers. This isn't changing at all.
The new one -- recital -- will exclusively use the online scoreboard. Like, it'll even do a check before the song begins to make sure it can communicate with the server. That way you're like a thousand times less likely to lose an awesome performance because of some firewall setting or because the server is down for maintenance or something. (The only thing it won't catch are momentary outages.)
Making the online scoreboard mandatory for that mode keeps things simple. (No "wait... is this getting posted online or not?" questions flying around, etc.) It also kind of fits with the name recital, where you're usually performing in front of other people.
I'm still working this part out, but I expect to be able to support anonymous scores in some form. Either nameless, initials-only, or just typing in whatever you want. I haven't decided yet. Though, the "real" way to submit scores is by using your Synthesia Talk (forum) account login.
All of this won't exist right out of the gate, but by using your account you'll be able to get cool statistics and other info on the website. Eventually there will be much tighter integration between the two that will make it an exciting proposition. At the very least, the sign-in info will be remembered and you won't have to type your name each time.
I had been considering forum-account-only access to the online scoreboard, but it's something I really want to see used heavily. And with the forum being this email-required, password-required, authorization email clicking, multi-step process... that seems like it might be a deal-breaker for a lot of people that aren't as motivated as you existing forum-goers.
By making it a seamless experience for both anonymous and forum-login players, I'm hoping it will see a lot of use.