Colloquial.
大 (big) +
半天 (half a day) = 'a big half-day' = 'most of a day, longer than expected'. Often hyperbolic in spoken Chinese —
等了大半天 may really mean just 'I waited a long time', not literally 6 hours. Compare
半天 (half a day / a long time) and
一整天 (a whole day).