Where the saving comes from
WebP's lossy mode uses prediction techniques borrowed from video compression: it predicts each block from its neighbours and stores only the difference. JPEG, designed in 1992, has no equivalent. The result is the same visual quality in fewer bytes.
The saving is largest on photographs with smooth gradients — skies, skin, shallow depth of field — where JPEG spends bytes on the very detail it then blurs. On busy, high-contrast images the gap narrows, though WebP still comes out ahead.