A dimensionless quantity is a number where the unit description (e.g, length, time, parsecs per lightyear) does not exist, usually generated by means of a formula in which all units cancel one another. For example, π is dimensionless because it is calculated as circumference divided by diameter – as these both have unit of length, they cancel out, and leave π. There are numerous other dimensionless numbers which have applications in physics, engineering, economics, etc.
A few years ago, I had too much free time, and decided it would be brilliant to write some code that would spit out meaningless formulas for dimensionless numbers. Seriously pointless. Feel free to click it a few times, and then lose interest as I did.