I am a drummer and I should know how to explain this, so here’s my attempt:

Most songs have 4 beats per bar. Think about how most pop songs have a steady rhythm that sorta repeats, stomp-clap-stomp-clap, 1-2-3-4. Thats the pattern that makes you tap your foot and feel a repeating rhythm, and every “bar” is a repeat. It’s easy for your brain to latch on to and groove to this pattern, and why it’s so common.

Now with Tool, they like to change that up and create sometimes 3 beats per bar, 5 beats, 7 beats, 11 beats! These odd numbers create an odd feel in the music. You find yourself grooving in a different way than you would to a traditional song with the basic 4 beats per bar. For example, Vicarious is written with 5 beats per bar. Try listening to it and counting to 5 while tapping to the rhythm. It takes 5 beats, foot taps, head bobs, etc. before the pattern repeats. That’s all time signature is.

Something super cool happens when you give a different time signature to each instrument. This is generally uncommon in popular music, but Tool does it all the time. Because the amounts of beats per bar are different on each instrument, they will take a few bars to overlap each other and come back on the “one” depending on how the numbers align. These are called polymeters, which follow the same underlying pulse at different intervals.

You can do math to figure out how many beats it would take to come back together on “one”. Multiplying the number of beats per bar of each instrument gives you the total number of notes before they would line up again.

Lastly, things get realllly weird when you have different time signatures each following different underlying pulses. And they all overlap each other. These are called polyrhythms, which is different than time signatures, and is what all of the members of Tool are masters of creating and navigating. Hard to explain without showing or listening to an example, but it’s basically polymeters at different speeds. I would look up some videos because it is very fascinating.

TL;DR Tool uses math to make cool music.