Yes and no.
Dynamic range is the range from the brightest white to the darkest black.
Clipping is indeed a big deal in digital photography, it happens quickly and you can't fix it in post.
It is the limiting factor of dynamic range in one direction, the brightest white.
In the other direction, the darkest black, it is signal/noise ratio.
In the darkest shaddows the light hitting the sensor is weaker than the noise from the sensor itself, rendering it useless since you can only see noise there.
However that's not as much of a deal as it used to be since any somewhat recent sensor has at least 12 stops between the brightest brights and noise eating up the shaddows.
That's orders of magnitude more than a .jpg can display and most scenes don't have that kind of dynamic range to begin with.
However as noise increases with ISO, it eats up more of your dynamic range at the low end.
At low to medium ISO it isn't realy noticeable since it is still more than your .jpg can show, but at higher ISO it gets noticeable if you want to do something on your exposure in .RAW.
To show scenes with higher dynamic range than your LCD display can show we can reduce contrast (looks terrible most of the time) or use tone mapping (also known as HDR).
Tone mapping essentialy keeps the colour information and compresses the brightness information to show you a better looking image with a higher dynamic range than your display can show.
(actualy it is a little more complex, but that's the basic idea)
Not realy an issue these days anymore unless you use an absurdly high ISO or fuck up your exposure.