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Free-fall time is the time it would take a body (an astronomical object, such as a cloud or disk) to collapse due to gravity if no forces opposed the collapse, e.g., no 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. Such uniform density has the interesting property (given the Newtonian mechanics approximation) that no matter what the radius, any such spherical body's free-fall time, no matter how large, depends entirely upon its density, such a collapse being termed a homologous collapse.
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 is dominating, and whether gravitational collapse might be capable of producing some observed phenomena.