Trouble understanding speed-dispersion in (elliptical) galaxies
The total light of a galaxy is the sum of perhaps billions of stars, each with their own line of sight velocity. You can characterise this distribution with a mean and a standard deviation (dispersion), and this will be reflected in the absorption line profiles of that galaxy.

Equally you might choose to measure this distribution as a function of position in a galaxy, if you are able to spatially resolve different regions. For instance one could put a spectrograph slit across a galaxy and get the velocity dispersion as a function of position along the slit.

When you are talking about nearby stars, you can measure the 3D velocities individually, providing you can measure the radial velocity, proper motion and distance of each star. You can then find the mean and standard deviation for this group of measurements in each velocity coordinate.