“He just released it over the weekend.”

You're telling your friend about a new song by an artist you both know, which was put up on YouTube on Friday. He doesn't know about it. You're explaining it, and you say:

He just released it over the weekend.

(someone) just (did something)

One of the uses of "just" is to express that something happened very recently. It can mean a few minutes before:

I'm sorry, he just walked out to go get lunch.

Or it can mean a few years:

Mankind has just started to study ways to understand and control DNA.

But in any case, "just" means a short time before.

release (something)

To "release a song" means to send the song out to the public, so that people can hear it and buy it. You can "release" songs, movies, books, and software. Another phrase with a similar meaning to "release ___" is "introduce ___". There's not a really strong difference between the two, but if you say that something was "released", it sounds like people wanted it a little more and were waiting for it. To "introduce" something sounds like more work! Also, individual people can "release" a product, but "introducing" a product feels like it takes a larger organization of people. Here are some examples of both:

Sony has hinted that they may be introducing a new tablet computer at next week's conference.

Kanye is releasing a new album in the fall.