Origins
Timber did not always mean wood. Old English timber meant 'building' — the structure itself, or any material used to construct it. Wood became dominant only because northern Europeans built almost everything from it. The material consumed the word.
The Proto-Indo-European root *dem- meant 'to build' or 'to construct'. It produced one of the most important word families in the Germanic languages. Proto-Germanic *timrą meant 'building material' or 'structure', and its descendants went in different directions.
German preserved the architectural meaning. Zimmer means 'room' — a built space. A Zimmermann is a carpenter, literally a 'room-builder'. The -z- in Zimmer reflects a regular sound shift between English and German (the same shift that turns English ten into German zehn).
Middle English
English narrowed the word to the material. By Middle English, timber meant wood prepared for construction — planks, beams, posts. The living tree and the finished building both vanished from the word's meaning, leaving only the substance between.
The warning shout 'Timber!' emerged from North American lumber camps in the 18th century, shouted when a felled tree was falling. It remains one of the most recognisable single-word warnings in English, even among people who have never set foot in a forest.