Deflection is the displacement of a member under load, and for the classic single-span cases it has exact elastic answers: 5wL⁴/(384EI) for a simply supported beam under a uniformly distributed load, PL³/(48EI) for a central point load, and wL⁴/(8EI) or PL³/(3EI) for the matching cantilever cases. The span enters at the third or fourth power, so a modest stretch in length produces a dramatic growth in sag — and a cantilever with an end point load deflects sixteen times more than the same load at the midspan of a simply supported beam.
Deflection is a serviceability check, not a strength check: a beam can be nowhere near yielding yet still bounce, crack finishes, or simply look wrong. Acceptability is judged against span-over-deflection ratios, and building tables bake such limits in — the 2021 IRC deck joist span table (R507.6) is computed for a 40 psf live load with an L/360 deflection limit, meaning the joist may sag no more than its span divided by 360.
Two modelling caveats travel with the closed-form numbers. They are Euler-Bernoulli solutions, which neglect shear deformation — accurate for slender beams — and they cover the applied load only, so self-weight has to be added to the distributed load explicitly when it matters.