The simplest kind of magnetic phase is a paramagnet, where each individual spin behaves independently of the rest, just like atoms in an ideal gas. This highly disordered phase is the generic state of magnets at high temperatures, where thermal fluctuations dominate.  Upon cooling, the spins will often enter a ferromagnet (or antiferromagnet) phase. In this phase, interactions between the spins cause them to align into large-scale patterns, such as domains, stripes, or checkerboards. These long-range patterns are referred to as "magnetic order," and are analogous to the regular crystal structure formed by many solids.
Quantum spin liquids offer a dramatic alternative to this typical behavior. One intuitive description of this state is as a "liquid" of disordered spins, in comparison to a ferromagnetic spin state, much in the way liquid water is in a disordered state compared to crystalline ice. However, unlike other disordered states, a quantum spin liquid state preserves its disorder to very low temperatures. A more modern characterization of quantum spin liquids involves their topological order, long-range quantum entanglement properties, and anyon excitations.