To “wait” on someone can have a couple of meanings. It can mean to wait, as in for a person to do something or to arrive at a particular place. Or it can mean to serve someone, as a waiter would. But in Isaiah 40:31 the word that in some versions of scripture is translated “wait” doesn’t really mean either of these things.
“But those who wait on the Lord…” What it means here is those who put their trust and their hope, in Him; those who completely rely on Him to keep His promises, and believe in Him wholeheartedly for everything He’s already said and done. These “shall renew their strength; they shall mount up with wings like eagles, they shall run and not be weary, they shall walk and not faint.”
God wants us to “wait” on Him, to hope in Him, to believe Him completely. When we do this, He is faithful to renew our strength to accomplish amazing things for the Kingdom.