Ryder Family Secrets
This mission spans pretty much the whole of the game. It kicks off after the events on Habitat 7- a sudden headache will send you to the SAM node back on the Hyperion.
Sam will fix you up, explain your new cybernetic situation, and unlock your dad's quarters down the hall. You can look at his stuff, grab the Normandy model above the bed, and look through his computer files (though most are locked). You can also investigate the odd glowing orb by the coffee machine.
This is a memory trigger. Despite the fact that SAM specifically says they are not tied to a location, each trigger you find in the future (are there are many) is location-specific. The more you collect, the more of your father's memories unlock, and the more of his files you can access.
These generally deal with the slow death of Mother Ryder, and the mysterious roots of the Initiative itself.
The Memory Triggers themselves are easy to find- they come auto-marked on your map everytime you discover a new planet. In general they like to appear atop high ridges and in outpost locations.
One exception is on Elaaden- the Trigger is inside a cave filled with monsters- the same cave you'll need to visit for the Cultivate task.
Gather them all up for Ryder to learn a little something about the Reaper threat, and the final fate of Ellen Ryder.
There is a side thread to this quest as well. As you continue to progress through the cluster, you'll unlock some moments with your twin. Mostly you can only ask the doctor about their progress, but shortly after completing Eos you'll actually be able to speak with them via SAM.
You'll have the choice to either lie to them about Alec Ryder or give them the truth. Either way they take it badly (now, or later), but they'll always end up forgiving you (the trail end of this choice pays off in the Journey to Meridian quest).