A Lyman-Break Galaxy (LBG) is a Galaxy identified as star-forming by the lack of radiation with Wavelength shorter than 912 Angstroms (Å), the Lyman Limit, i.e., the lower limit on wavelengths in the Lyman Series. Neutral Hydrogen (H) around Star-Forming Regions (SFR) absorbs the radiation.
This method of identifying star-forming galaxies is largely used at Redshifts (z) of Z in the 3-to-4 range, using filters on the redshifted spectrum. The method has the advantage that the "break" causes Dropouts, i.e., images through some filters don't show the galaxy, providing a relatively easy way to identify them by comparing the filtered images, that the break is visible through the Earth's Atmosphere within the 3-4 redshift range, and that the redshift can be determined with some precision using subsequent Spectrography to identify the wavelength of the observed break.
Balmer-Break Galaxy (BBG)
Brightest Cluster Galaxy (BCG)