For a piece to be visually intriguing and conceptually fascinating; Simplicity, color, patterns, and edges are what I like to see.
An excellent example of simplicity would be Toshiko Takaezu bottle, when scrolling through the collection on accessceramics.org, this piece immediately caught my eye. Nothing could be as simple as this piece other than just a regular bowl, the spherical shape reminds me of early pottery and its functionality its outstanding.
Another aspect that I mentioned would be lots and lots of color, a piece that has eye popping color right off the bat grabs my attention more than any other pieces. Example of a piece with great color would be a vase that Gene Bunker made back in 1957. This vase has so many colors working at once, it grabs my attention and has a great way of being visually intriguing.
The third concept would be that the piece has patterns, a piece with patterns has that classic feel that everyone is familiar with. Patterns have always been a very important aspect of art, dating as far back as records can show. This image shows a great example of patterns being taken full advantage of, this piece is titled "The Fragility of Belief" by Eliza Au.
The fourth and final aspect are edges. I really like looking at pieces that have lots of sides, angles, and edges. I find these pieces visually pleasing because of the many different ways you can view that one piece. Every angle or direction you look at the piece, you see it differently than the way you viewed it before. This piece was designed and made by Alison Petty Ragguette, and is titled "Visceralab Installation".
With these four visually intriguing and conceptually fascinating keys in mind, these are what make me want to look at more and more pieces to get senses and ideas of what kind of art I like, and would like to create.