Galactose is a six-carbon sugar. A galactoside is any compound such as lactose that when hydrolyzed yields a galactose molecule. So a galactosidase is an enzyme that catalyzes the splitting off of galactose from a larger compound. In this case, the larger compound is lactose. And in this case, if the galactosidase acts on lactose, it is also then a lactase.
Some adults lack lactase.
The main symptoms include gas and flatulence. One approach to managing milk intolerance is to avoid dairy foods. Another approach is to get extra lactase. Lactase can be added to milk or it can be swallowed by the person. The idea is to convert lactose to glucose and galactose early in digestion.