In the scene prior to the final London fights, Shepard gets to talk to all his companions. When talking to Liara, she offers him a gift, and upon accepting they both are shown on a entirely black background with some stars spinning around them and a blue light that looks like an accretion disc or a galaxy in the distance.
What was that all about? I assume it was some Asari mental ability, but what exactly did she do and why?
Well, when i first got to that scene, i just tought it was her way to show me something special, since i romanced her, before the final fight. But then, after the second time (with no romance) she did it again.
This is what comes up from a search on masseffect3 wiki:
Regardless of whether a romance is pursued with Liara,
before the final battle in London,
Liara gives Shepard a gift: joining her consciousness with Shepard's
to share an intimate moment,
a practice that is normally reserved for good friends or a bondmate.
Also i remember reading on bioware's forum (sorry i don't have that link anymore, if i'll find it i'll update) that it also served as a sort of time-capsule, on which Liara "saves" Shepard's memories for future generations (this makes sense too, since the scene's background changes if you're renegate/paragon oriented, so it fits your character)
naive fan theory: her gift was to render shepherd unconscious and save him from his fate. The whole rest of the ending was a dream. The result of the end fight is unknown but Liara somehow knew what his fate would be and kept him from it, perhaps even kept herself from it. maybe realizing it was entirely hopeless, In a moment of clarity she decided it would be better if he only beleived that he saved everyone, as reality itself was much more dire to face.
