Although Yoda was a major player in the Star Wars prequel trilogy last decade, the fact of the matter is that chronologically, the character has been dead for decades. Yoda passed away of old age during Return of the Jedi, but like Obi-Wan Kenobi before him, he still lives on as a Force ghost. In the lead-up to Star Wars: The Last Jedi, it was rumored that Yoda would appear, and sure enough, the small, green, Force sensitive whatever-he-is showed up in his spectral form to dispense one last piece of advice to Luke Skywalker. Rather than make Yoda an all-CGI creation again, the Jedi Master was once again performed as a puppet, and as you'll see in the video below, seeing that puppet made Mark Hamill emotional.
One of the special features attached to Star Wars: The Last Jedi's home release (and also aired at SXSW this past weekend) is a feature-length documentary called The Director and the Jedi, which follows Rian Johnson as he stepped into the world of Star Wars for the first time to oversee the most recent Star Wars movie's production. In this clip (posted by Star Wars Legacy), we see Johnson and Mark Hamill nearby as one of Yoda's scenes is being performed by the character's longtime voice and primary puppeteer, Frank Oz. Judging by Hamill's reaction, this moment undoubtedly reminded him his time with the original Yoda puppet when he was working on The Empire Strikes Back and Return of the Jedi all those years ago. It's also nice to see Hamill and Oz properly reunite after the scene is finished, with Hamill pointing out that Oz has aged more gracefully than him.
Star Wars: The Last Jedi marked the first time that Frank Oz has operated an Yoda puppet since 1999's The Phantom Menace (although newer versions of that movie have since replaced Yoda with a CGI version so that he matches up with how he looks in Attack of the Clones and Revenge of the Sith). As for Hamill, although he made a voiceless cameo in The Force Awakens, The Last Jedi marked his full return to the world of Star Wars, where he reunited not just with Oz, but Carrie Fisher as well. Filming a Star Wars movie is a big deal for anyone involved, but for Hamill and Oz, it was especially important.
Yoda popped up in Star Wars: The Last Jedi shortly after Rey departed Ahch-To to counsel Luke when he was deciding whether or not to burn down the tree containing the sacred Jedi texts. When Luke decided against it, Yoda cast a bolt of Force lightning and did the deed himself, telling Luke that it was up to the Jedi themselves, not books, to pass along knowledge of the Force (though what Luke didn't know was that Rey had already taken the texts and packed them aboard the Millennium Falcon). Luke and Yoda then shared one more moment together, and with Luke later passing away after Force projecting himself to Crait, he now gets to hang out with his former master in the Force netherworld.