Research parts are falling components of your spaceship.
When they begin to fall you will get the mission display in the top right 'Orbital debris incoming'.
They can either be tracked through the sky, or found later by looking for plumes of smoke and flashing beacons. The smoke will appear reddish when you are close to the drop pod.
Once you have found the drop pod there will be a small box. Destroying this will yield one research part.H.O.D.O.R can be used to cause orbital debris to fall.