Basically, SEGA likes to pretend they own part of it, but they don't.
All of this is based on a vocal synthesizer program called Vocaloid. Miku Hatsune is basically the mascot for the most popular of the programs (the characters are named after the program they are the mascot for). The programs have been around for at least 4 years, and there's at least 20+ official Vocaloid programs, plus tons of fan made, and troll programs made from everything from 2ch's VIP board, to just random users making their own solo projects.
So there's literally thousands and thousands of songs made by random users for each Vocaloid, and they cover tons of different genres. Each Vocaloid has a set recommended tempo, genre, and so on, and they each come with a Japanese voice, male or female, or in some cases, they are made bilingual, like Luka Megurine. And to be honest, most of the fan made songs are way, way better than any of the official music, since fans com up with way more variety for what they compose. Most people that compose with Vocaloid upload the songs along with PVs they made themselves onto Nico Nico extremely often. A few people even got edited versions of their songs into the games, and into the concerts.
SEGA made 4 games based on the music (one of them won't be out until this Summer), which are all rhythm games, and they were one of the sponsors for the concert from the videos posted. So because SEGA puts Miku as a cameo character in alot of their games, they like to pretend they own rights to Vocaloid, but they don't at all, as far as I'm aware.
And Miku Day is March 9th, and it's a recognized holiday in Japan, but not official or anything. It's that day since 39 can be read as Mi-Ku, and they make tons of 39 puns and references for media involving her. And since she's the most well known, and overall most popular with fans, she's pretty much the figure-head for Vocaloid.
I've been a huge fan of Vocaloid for around 3 years now, so I know tons of useless info about all this stuff. lol There's tons and tons more info about all this, but that would take forever to cover, so I hope this helps a bit.
If you want to check it out, here is the Vocaloid wiki.
Link
If you want to check out some more songs, this Youtube channel uploads stuff from what Nico Nico users make pretty often, and usually posts around 5+ songs a week.
Link.
