The story
Old English said dohtor, and the H in the middle was a real consonant — a rough, throaty sound like the ch in German Tochter or Scottish loch. German Tochter and Dutch dochter are the same word, and they still pronounce it. The word is very old: it goes back to the same ancient root as Greek thygátēr.
In Middle English the word was written doghter or doughter, with gh standing for that throaty sound. Later, in late Middle or early Modern English, the sound disappeared from most English speech, as it did in night, taught and bought. The vowel before it shifted, and the word settled into something close to today's "DAW-ter".
The spelling daughter had already been fixed, so the GH stayed on the page — a silent marker of a sound English speakers really used to make.
