I am not sure if "Beats" refer to "heart beats" or "music beats". What does the title mean as a whole?
This will include spoilers from later in the show, for anyone not wanting to spoil, please don't read my answer, just know that it in fact is both of the suggestions @An hoa has.
It's both Heart Beats and Music Beats
Your assumptions of it being one or both of the two suggested is correct, as the title as a whole is a play on the fact that the whole show revolves around a character Otonashi who's heart was given away, to the girl Kanade, after he had died. (or Tenshi, for those of you who don't like her actual name).
In the end of the show we see that Kanade thanked Otonashi for giving her the heart she had used to carry on living. She had always wanted to thank him for the beating heart she had been given, as hers was no good.
We all realized that it was referring to the beat of the song, as well however from the get go, due to the catchy rythm of the OP. So it's natural to think that that was the reasoning. However it IS both.
The title literally means The beating of Kanade's heart
As we know Kanade is known as Tenshi which directly translates to Angel.
In the last episode of Angel Beats!, Kanade thanked Otonashi for the heart that he gave to her. Kanade, a.k.a. Angel, said that his heart was still beating in her chest, and that when he had fallen asleep on top of her chest, he was listening to the rhythm of his own heartbeats. This is the meaning of the anime's title.