In introducing someone to Phish, it's important to set the ground a bit first and not just start playing the music. First off, Phish is a modern-day vaudeville act. That is, each show has many parts and there are many narratives woven throughout Phish's catalog. There are jokes, pure absurdity, and lots of antics one should expect. This is not something to "get past" but something to embrace. It's basically a reminder not to get too serious no matter what or you'll lose your ability to have fun, like Wilson the Duke of Lizards did and like the Book written by the great and knowledgeable Icculus tells us - by the way, you must Read Icculus. Ridiculous, right? There you have it. That's part of the fun.
But it goes deeper. There are also stories within stories. There is an entire album's worth of songs, Rift, which is essentially about a tragic divorce and all the anger and sadness and loneliness that led to it and came from it. That's not funny stuff at all. But it's there. And it may emerge as a major theme in your next show. There are religious and spiritual references, as in Ghost or Bug.
There are songs about getting lost in too much of a good time to have a good time, as in Joy or Sparkle. In essence, real life abounds in the songs and I am speaking specifically about the lyrics.
But never are the lyrics so direct as to be forceful - like the music itself - it is always open for interpretation and new meanings. It's part of the mystery and enjoyment in a Phish to figure out what it means to you at the moment in your life. It changes over time.
Then there is the music. Phish are one of the most technically proficient rock bands to ever take a stage. They have rehearsed complex and lengthy original compositions to the point where they can play them note-for-note in their sleep and still manage to completely tear the roof off an auditorium. They do often play their more complex pieces, like say Divided Sky, exactly as it was written almost 30 years ago. That proficiency is impressive but it's not all they do. That level of intricacy and musical understanding is the basis for which they take off into jamland and it is what makes them different from any other "jam band" out there - a genre I pretty much can not stand save for Grateful Dead and Phish, because other bands just play three freakin chords for 30 mins. Phish can literally go anywhere at any time and neither the audience nor the band has advance notice of where that will be. Given that they can make you laugh, make you cry, make you scared of your best friend who is standing next to you at a show, or make you want to hug a stranger in the aisle - it's thrilling. As long as you are there to enjoy the ride, and not bound to a particular destination, there is no other live show that can compare. You will enjoy yourself beyond measure if you take it all in stride.
As for the name, Phish, it is not merely a reference to the drummer but also a reference to all of the above. They aren't married to a style or sound, they are out there on stage with a Mary Poppins size bag of musical tricks and they are fishing for what comes next, what sums up the feeling between themselves and in the audience, in essence, what is the musical statement that takes everything we can see, feel, and know about that night, and best communicates it for the collective experience. That's what Phish does. And never too seriously as to be mistaken for complete assholes.