This is a Dyson style post-motor pleated filter assembly for the V10 and SV12 range of battery operated stickvac vacuum cleaner. It's in a bright purple and fits at the back of the motor on the pistol grip.
They click off and on with a short 10 degree twist.
They suit the V10 Cyclone Series, the V10 Absolute and V10 Absolute and the V10 Animal and V10 Animal and the V10 Motorhead, and the V10 Total Clean as well as the Dyson SV12
NOTE: If the filter is badly blocked, such as in the fourth photo, it will cause the stickvac to stop, or not run at all, and the battery lights will flash alerting you to the filters condition.