Liam suggests the crew would enjoy a relaxing movie night.
Once you have gathered all of your squad members on the Tempest, talk to Liam to acquire this mission. You receive an email from him as well, but it's not required to read first.
Get a movie library download from the Nexus Edit
In the Operations section of the Nexus, head to the marker in the room next to the prison cells. There will be an archive system in the back. Using it will give you the movie library you need.
Return the movie library to Liam on the Tempest Edit
Talk to Liam on the Tempest to give him the movies. He says he'll look through them, and the mission will be complete.
270 xp (doesn't show on screen).