Why A linear regulator works by acting as a variable resistance (a pass transistor) between input and output, so it can only throw away voltage, never add it. The dropout voltage is the smallest input-to-output difference the pass element needs in order to stay in its active region and keep the output regulated. Classic 7800-series parts need roughly 2 to 3 volts of headroom; low-dropout (LDO) designs get this down to a few hundred millivolts or less. If the input sags to less than output plus dropout, the output simply follows the input down and regulation is lost.
Watch out The choice about maximum output change as input varies describes line regulation, and the one about output decrease at rated load describes load regulation. Both are performance specs, not the minimum headroom requirement.
Dropout = the headroom a linear regulator needs. Input must stay above output plus dropout or the regulator 'drops out'.