The actual Hebrew word for "wait" in this verse is QAVAH, which indeed means "to expect." But Hebrew words are also little pictures, revealed often by the meaning of it's Root word. When a Semitic person hears a word like "wait", they are not just hearing the word itself...or it's "meaning"...but it is like a little motion picture moving in his head, on the screen of their imagination.
in my opinion, this picture is revealed when you see that this ROOT WORD is translated into English from the primary concept of "twisting together."
QAVAH means "to bind together, by twisting...as in a rope." Therefore, to "wait on God" is not passive, like "just sitting and waiting for something to happen." The Puritans did not believe in passivity for a good reason...it's not biblical.
Rather, the idea is that to "wait on God" Hebracially means that you allow the LORD Himself and His thoughts to interweave with your life. In other words, you are waiting on God as you prepare yourself by scripture study, meditation, prayer and renewing your mind continually.
The picture is also one of "a vine that twists itself around a tree trunk." A picture of strength and dependence on Another. Literally: active participation together where the two become one.
This is the same word used in the well-known verse in Isaiah 40:31, "But they that wait upon the LORD (lit. "they who have there lives so intertwined with GOD in every way possible")...they are the ones "who shall renew their strength: they shall mount up with wings as eagles: they shall run, and not be weary; and they shall walk, and not faint."
Hebrew is a dynamic language, and not static; it is a language of great emotion and evocative images. Hence, in Psalms 130:4-5 we "expect" because we are "twisted together" with our Creator, the One who made us. And He will answer His elect when they cry out to Him. Rather than taking matters into our own hands, we wait on Him.