Free-fall time is the time it would take a body (astronomical body including a cloud or disk) to collapse due to gravity if no forces opposed the collapse, e.g., gas pressure. The term free-fall timescale (or dynamical timescale) means essentially the same thing but might imply a more general estimate. This time is dependent upon the mass and distribution of the matter and can be used in some calculations of processes dependent upon these qualities. Free-fall time for specific configurations such as a sphere of known size and uniform mass density have well known formulae with well-known derivations.
Estimating free-fall time is useful for producing an order-of-magnitude regarding the necessary time for an event, e.g., the collapse of a cloud into a star, or time involved in a core collapse supernova. In other words, are we talking seconds, days, decades, or millions of years? Such rough estimates help direct modeling, help tell you if gravitational force could be dominant, and whether gravitational collapse might be capable of producing some observed phenomena.