In the most basic sense:
1D = A single row or column
2D = A range of cells, with multiple row(s) and/or column(s)
3D = Range of cells like 2D, but spanning multiple sheets.
The visualization of 3D is to picture all of your worksheets stacked on top of each other, and you make a range that goes through all of them. Bobhc already posted some good reading material on differences as well.
Last note, when calling it an array, some functions within XL naturally expect a single output/input. I.e., the IF function normally expects a single input and single output. You can however use Ctrl+Shift+Enter to make an array formula, which just tells those functions "Hey, I'm giving you more than 1 cell, you need to look at all of them".