Tai tai is a traditional Chinese term for the senior wife in a family that might also include other wives and concubines.
"Tai" is usually translated as "supreme". The English word "typhoon" is from "tai feng", supreme wind. Mandarin "tai ban" is the "big boss"; the Cantonese form Tai Pan is the title of a well-known novel. "tai tai", then, is "supreme supreme".
In current speech, either Chinese or the English of China expatriates, "tai tai" is often used for the well-off females who spend much time shopping, mostly for luxury brands.