Destiny launched back in September 2014, with a major push in particular on the PlayStation 4 as the console of choice. But it also arrived with a decnet performance on legacy platforms the Xbox 360 and PS3 and those formats have been supported for the last two years.
Now that's about to change. An update due out today will be the last made available to older generations:
"Before the launch of Destiny: Rise of Iron on September 20th, there are a few issues we are fixing. This update will also be the last scheduled deployment for Legacy Consoles, excluding emergency fixes for future game-breaking issues."
After this update, you won't be able to share your progress from one console generation to another and certain trials will no longer be available. It has to be stressed though that the game will still work on Xbox 360 and PS3, you just won't be getting new content drops anymore.
This move has been on the cards for some time, and Bungie has actually done a decent job of keeping these older consoles (which were already a year out of date at the launch of the game) up and running. For now, enjoy what's left of that life cycle and maybe consider an upgrade if you want to keep playing.