Uuuuuhhhhhhh...that nks for the nightmare! That's permanatly stuck in my head now!
-vinyl- WTF LYRA! U have...SOMETHING THATS NOT HOOVES! O.o -Lyra- I KNOW! ISNT IT GREAT?!?! -vinyl- okaayyy...*turns slowly then nightmare moon in her face* -nightmare moon- heeeyyyyyyy vinyl! -vinyl- (thinking) shit
The Season One, Episode Seven show "Dragonshy" showed Lyra (official name Heartstrings) slouching on a park bench in a very human posture (around the 2:19 mark).
This single shot was picked up on by the fandom, and turned into a running joke about Lyra adopting human behaviors in general. This then evolved over several months into "Lyra wants to be human" and then "Lyra wants hands".
The meme is strengthened because it's also a gentle dig at some of the logical inconsistencies and problems ponies might have using the kind of human artifacts which are very common on the show - everything from cider mugs to a piano. Thus, a very logical pony might conclude that operating a lot of daily things might be easier with hands like dragons, serpents, and minotaurs have. This very amusing potential heterodyned with the "Lyra acts like a human" meme and Lyra is now the unofficial go-to character for anything to do with ponies wanting to be human or have human anatomy, acting like humans (where this is different from acting like a FiM pony), referring to phrases which reference nonpony anatomy like hands or feet, and so on.
(This has also bled over into jokes about Lyra collecting "My Little Human" figures from her favorite show, being the pony equivalent of a furry, and so on.)
(It's also related to the memes about Lyra being something other than a unicorn (a "sea pony" form is common), and human versions of Lyra wanting to be a pony, which is itself a dig at some of the more extreme fandom aspects.)
Pony massage is a known method of relaxation on the show. The spa ponies offer it and we've seen Rarity and Fluttershy getting massages.
"Magic Fingers" (the link) is the brand name of a massaging function in beds which used to be more common several decades ago. It kind of died out as it was fairly crude (more a general wobble/vibration than any kind of actual muscle massage), but the brand name lives on in pop culture remnants from that era.
Lyra in the pic has just used unicorn powers to create "magic fingers". Of course she's going to want to try them out! And fingers are better massage implements than hooves, so what better test? And who better to give her feedback than Bon Bon, the pony Lyra hangs around with so much?
So the link is a pun on the image, although it works better if you've heard of the brand name before.