Listening to tracks is obviously a crucial facet of any time spent on thesixtyone.com, but the technical definition of what counts as a listen for the purposes of quests (eg. Refined Taste), achievements (eg. Listen Up), and the total “plays” count on a listener's page is harder to pin down. The following is one working theory, based on some hours of testing. ← more experienced listeners, please edit and correct/refine this!
Time spent listening is counted, regardless of where in the song you listen. For example, listening to the last half of a song will count. You can also, for another example, listen to the first minute of a 4 minute song twice in a row (using the progress bar in the player to jump around) and it will count as a listen, as soon as the cumulative time spent listening to a track meets one of the thresholds described in the points above.
The “now playing” status at the top of a listener's page will update to the current track at the same time the listen is recorded. Updates to both the “plays” count and the “now playing” will often not be displayed until you navigate away from the listener page and return, not by refreshing the page, either using browser refresh, or clicking a link within t61 that would reload the page, nor using t61's navigation arrows in the upper left corner.