A compound is considered a strong base when its conjugate acid is relatively stable. In the case of OH-, its conjugate acid (HOH) is very stable. So it is a strong base.
A compound is considered a strong acid when its conjugate base is unstable, and vice versa. (CH3)3-C-O is a very strong base, and strong nucleophile. It is very readily to react with other electrophiles. In addition to that, (CH3)3 is an electron donating group which also contributes to the strong basicity of tert-butyl-O-.