Have you ever wanted to be able to touch your toes easily? Have you ever wanted to do the splits? Maybe you want to kneel comfortably, or touch your hands together easily over your head.
Being flexible, makes things easier. The more flexible you are the easier it is to do more things.
Flexibility isn't floppiness
Note that the flexibility I am describing here isn't floppiness. Instead, it's the ability to do more things with control. So being able to touch your toes, or the splits while using relevant muscles to control your body while you do it.
It's the difference between being like a piece of string, which is floppy, versus an elastic, which bends, but resists being bent so that it can return to it's pre-stretched position.
Flexibility is control across a wider range of movement
And so being flexible means being able to bend over and tie your shoelaces. But it also means being able to bend over, pick something up and not hurt yourself in the process. It can mean being able to do those high kicks that look cool whether in martial arts of dance class. It means being able to do more of those yoga poses that you always thought where impossible or take a lot of time to achieve. For example, binding.
Becoming more self-reliant
Being flexible in a yoga class means that you don't have to rely on props. (And nothing against props, they are great tools for helping to get more flexible, but like training wheels on a bike, it's nice when you no longer need them.)
I know what it's like to be inflexible. I was inflexible for almost 30 years of my life. And while yoga helped a little bit, it wasn't until I began to explore and understand muscle control that I began improving my flexibility more consistently.