The shirt is a play on a design meme popular a few years ago, where related words or names are listed in Helvetica font with ampersands in between them, and a period after the last one. (The meme originated with a Beatles T-Shirt designed by a Dutch company.)
The words on Ariel's shirt all come from The Little Mermaid movie. Ariel likes to collect human artifacts. She calls them her treasures, but doesn't know what they are. She believes her seagull friend Scuttle knows all about humans (he doesn't, of course), and asks him the name and purpose of the things she finds. Since he doesn't actually know any more about humans than she does, the names he gives are nonsense words (dinglehopper, snarfblat) or words used as placeholders when you don't know what something is called (gizmo, whooz-it, whats-it, thingamabob).
I've got gadgets and gizmos a-plenty
I've got whoozits and whatzits galore
You want thingamabobs? I've got twenty!
"Part of Your World" lyrics
(From watching that song a few times, I've determined that a gizmo is a pocket watch, and thingamabobs are corkscrews. I can't figure out what object she's holding when she says "gadget" - it's something diamond-shaped at the end of a string. She sings "whoozits" and "whatsits" off-screen, but it's possible one or the other of them is used for eyeglasses, since that's what's shown when she sings those words.)
Scuttle also tells Ariel utter nonsense about what the items are used for. For example, when Ariel shows him a fork, he says,
It's a dinglehopper. Humans use these little babies to straighten their hair out. See? Just a little twirl here and a yank there and voila. You've got an aesthetically pleasing configuration of hair that humans go nuts over.
Similarly, about a smoking pipe:
Scuttle: I haven't seen this in years, this is wonderful!
Ariel: What is it?
Scuttle: A banded, bulbous snarfblatt.
Ariel, Flounder: Oh.
Scuttle: You see the snarfblatt dates back to pre-hysterical times when humans would sit around and stare at each other all day.
Scuttle: got very boring. So they invented this snarfblatt to make fine music, allow me!