I’ve read that real numbers are numbers that can represent a continuous quantity in a number line. What does continuous quantity mean?

Answer 1

"continuous" means no gaps, no breaks, no discontinuities

you can draw the real number line without picking up your pen or pencil

if you picked out a point on the number line, it would correspond to some real number

the real numbers are all next to 2 other real numbers, on each side, with no space between them