The Doppler effect is the change in frequency of a wave in relation to an observer who is moving relative to the wave source. In astronomy, it is used to measure the speed at which stars and galaxies are approaching or receding from us (blueshift or redshift).
The Solar Neighborhood contains stars within a few light-years of the Sun. These include Proxima Centauri, our closest stellar neighbor, and other systems that help us understand stellar evolution.