Origins
A ladder is something you lean β and that is exactly what its etymology says.βββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββββ Old English hlΗ£der traces to Proto-Germanic *hlaidrΔ«, from PIE *αΈ±ley- meaning 'to lean'. Strip away a thousand years of sound change, and a ladder is simply 'the leaning thing'.
The word has changed remarkably little. Old English hlΗ£der lost its initial h- (as most English hl- words did) and became Middle English laddre, then modern ladder. German took a parallel path: Leiter, from the same Proto-Germanic root, is still the standard word.
The PIE root *αΈ±ley- produced an unexpectedly wide family. Lean is the most obvious relative. Incline adds the Latin prefix in- to the same root. Decline is leaning away from. Recline is leaning back.
Latin Roots
The most surprising cousin is climate. Greek klima meant 'slope' or 'inclination' β specifically, the angle at which the sun strikes different latitudes. Ancient geographers divided the world into klimata, zones of solar inclination. The word passed through Latin into English as climate, meaning 'the weather characteristic of a latitude'. A ladder leaned against a wall and the climate of northern England share a root because both describe an angle of inclination.
In British English, a ladder also means a run in a stocking β the visual resemblance to the rungs of a ladder giving the damage its name.