Maz giving Finn the lightsaber is noticeable for many reasons, not least of which because it happens twice and for all the Arthurian parallels surrounding the scenes.
The first time takes place just after the destruction of the Hosnia system which is what makes Finn return to Han (and implicitly to the fight against the Dark Side). At this point none of them knows that they’re about to be attacked themselves by the First Order, not even Maz.
Despite this she immediately upon Finn’s return takes him, Han and Chewie into the cellar where she keeps the lightsaber. When she takes it out of the chest Han recognizes it and asks where she got it, she brushes him off and focuses on Finn.
Why Finn? Last she saw him Finn made it clear that he was leaving. Hosnia’s destruction marked a tentative return, but so far it is tentative. And wouldn’t Han a man who might not be a paragon, but someone she’s know for years, make more sense?
Her words as she passes it are ambiguous. “Take it. Find your friend.” And do what exactly? Give it to her? Use it to protect her? What? Recall, no one but Maz and Rey herself knows that Rey can use the Force at this point. In fact Finn is never told this in TFA.
In assorted other things the fact that Han’s attention shifts off Maz and onto Finn the moment she tells him to take it, but before she stops talking is interesting. His intent gaze on Finn as he makes the choice to take the weapon is mirrored in the second “giving” by Maz.
Maz too is looking rather expectantly as Finn reaches out and takes the lightsaber from her. The music that has so far been playing softly in the background swells dramatically the moment Finn’s hand touches the saber and mixes with the diegetic sound of an approaching TIE fighter as Finn raises the lightsaber as a young Arthur might Excalibur. The scene ends in a dramatic boom as the castle is struck just as we see Finn look at the saber with a serious face.
It is noticeable that Finn is so entranced by the lightsaber that he doesn’t seem to hear the incoming TIE. Not long before at Niima Outpost he jumped at the first sound of it, but here he’s oblivious to the noise.
Now before I go on to the second “giving” I’m going to make a small detour around Arthurian myth.
Much have been made of the Arthurian parallels in TFA. Kylo Ren as a Mordred like figure. Luke as either a Merlin or a fallen Arthur himself and of course Rey pulling the Skywalker lightsaber out of the metaphorical stone. But the Arthurian parallels have been ignored where Finn is concerned, especially when it comes to the giving of the lightsaber/Excalibur, because in Arthurian myths there are two kinds of givings of that sword. One is Arthur pulling it out of the stone which declares himself the true king of Britain, in the other it is given to him by The Lady of the Lake.
In both versions Arthur starts out as a youth of unknown parentage grown up fostered by strangers, just as Finn is. In the second versions Arthur runs into Merlin, often portrayed as an older, wiser man. Depending on the version Arthur either asks Merlin for help or about his future, in either case Merlin takes him to The Lady of the Lake.
The Lady depending on the version of the tale is either a powerful magical being or a High Priestess of Avalon. She proceeds to ask the young Arthur several question and put him through a test which he fails, but she sees that though he is not perfect he has a good heart and a true spirit. Realizing this she bequeath him Excalibur, the sword of the true king and the mark of a hero.
Maz is in a quite literal sense The Lady of the Lake. She a powerful alien, strong in the Force who has made her home on a lake.
Her initial interactions with Finn runs parallel with The Lady’s testing of Arthur, complete with Finn “failing the test” by choosing to leave. But in deciding to return to the fight Finn proves to The Lady of the Lake that he’s heart and spirit is true and so she gives him Excalibur (the Skywalker lightsaber) to wield.
That she means for him to wield it and not just as a caretaker becomes clear in the second “giving”.
When they exit the now ruined castle the dark forces are upon them and battle is joined. Maz once more tells Finn to go find his friends.
This time Finn has no intention of leaving proving him once more worthy of Excalibur and this time Maz’s words are unambiguous, she intends, and always intended, for him to be a wielder of the blade, not just a carrier.
As Finn again lifts the Skywalker lightsaber and this time ignites it, Maz look on with great expectancy clearly meant to mirror the audience. Will “Excalibur” accept Finn as its wielder? And will Finn accept the lightsaber as his?
At first we see doubt on Finn’s face, it’s an unfamiliar weapon and a Jedi’s weapon to boot. How can he wield this? But Maz believes he can and Finn is nothing if not up for whatever challenge life throws at him so he ignites it. The blade flashes to life in his hand, accepting him as a worthy wielder, and the moment it does Finn’s decision is also made. He may not be a Jedi (yet), but the sword is his.
tl;dr. There is a lot of Arthurian coding around Han (Merlin) bringing Finn (a young Arthur) to Maz (The Lady of the Lake), Maz testing him and in finding that he has a good and pure heart gives him the Skywalker lightsaber (Excalibur). The sword allowing itself to be ignited (drawn from the sheath) confirms Finn’s worthiness as its wielder.
