A Lyman-Break Galaxy (LBG) is a Galaxy identified as star-forming by the lack of radiation with Wavelength shorter than 912 Angstroms, the Lyman Limit, i.e., the lower limit on wavelengths in the Lyman Series. Neutral Hydrogen around Star-Forming Regions absorbs the radiation.
This method of identifying star-forming galaxies is largely used at Redshifts 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)