Mirrorless cameras are exactly as described, digital cameras without a mirror! Since the rise of digital, DSLRs have been the dominant type of interchangeable lens camera. After upgrading from a point & shoot, or if wanting to start photography, a DSLR was more or less your only option.
Not anymore! With modern advances in technology, cameras can be made that don’t use a mirror between the lens and sensor. These cameras generally use electronic viewfinders (EVF) to replicate the through-the-lens view a DSLR gives you.
Companies like Olympus, Panasonic, Fujifilm, and Sony have invested heavily into mirrorless technology, pushing it to the forefront of the camera world and overtaking DSLRs in sales. Even SLR stalwarts like Canon and Nikon have begun to take mirrorless seriously, introducing their own professional-level mirrorless cameras.
Mirrorless cameras have very short flange distances (the distance between the back of the lens and the digital sensor) because they have no mirror. A big advantage of this is that you can easily adapt vintage lenses from almost any system imaginable.