Full-frame equivalent is the focal length figure that describes what a lens's actual field of view would be if achieved on a full-frame sensor, letting focal lengths be compared meaningfully across different camera formats.
Full-frame equivalent is the focal length a lens behaves like once its actual field of view is translated to a full-frame sensor, and it is the number photographers reason with when they call a lens wide or long. Camera makers print the true focal length on the barrel, which is honest but not directly comparable between formats, so a 17mm Micro Four Thirds lens and a 34mm full-frame lens frame identically despite the different numbers.
Without converting to a shared reference, a smaller-sensor system's lineup is hard to judge: is that 12mm lens wide enough for landscapes, is that 45mm right for portraits? In equivalent terms they are 24mm and 90mm, which answers both questions at once for anyone who has shot full frame. The same logic lets someone moving between an APS-C body and a phone, whose main camera is often around a 24mm or 28mm equivalent, picture what each will capture before raising it.
A photographer researching a compact travel setup sees a Micro Four Thirds 100-400mm zoom and a full-frame 100-400mm zoom at similar prices and assumes they are equivalent. They are not: the Micro Four Thirds lens has a full-frame-equivalent range of 200-800mm because of the 2.0 crop factor, so it reaches twice as far. For a wildlife trip that is a strong argument for the smaller system.
For a portrait photographer wanting an 85mm-equivalent look, the same 2.0 factor means reaching for a 42.5mm lens, a number that means nothing until it is converted to the 85mm most portrait shooters picture. A 50mm 'nifty fifty' bought for that body would actually deliver a 100mm-equivalent short telephoto, useful but not the standard-lens look the name implies. Aperture behaviour does not scale the same way: that 42.5mm f/1.8 gathers f/1.8 worth of light for exposure but renders depth of field closer to an f/3.5 lens on full frame at the matched framing.
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