The song in question is "Landslide" by Fleetwood Mac, which comes from the band's self-titled 1975 album. According to Genius, Stevie Nicks actually wrote "Landslide" as a metaphor for her fears that everything in her life could come crumbling down in an instant. Inspired by the mountains in Aspen, Colorado, Nicks illustrates this fear by singing about an avalanche that sends her crashing back down after she's climbed a mountain.
While at first glance this metaphor may not seem to have much to do with the scene itself, the gentle guitar and lyrics like "But times make you bolder, even children get older" help to emphasize the way in which this dinner is the start of a new, happier future for all. It also helps represent that, although the group has achieved peace at long last, they're still living in a world wherein everything could come crashing down at a moment's notice.
As such, it's important to cherish these brief moments of happiness amidst the post-apocalyptic world surrounding them. The inclusion of "Landslide" in this dinner scene helps to set the tone and usher in a new era in the world of "The Walking Dead" — one which embraces life more than death.
