When Philip asks Jesus, "Lord, show us the Father, and we will be content," what is he asking for? Obviously his categories were mistaken, because the answer to his request was standing right before him; but what was he anticipating Jesus would do? Was his request along the same lines as Moses' request, "Now show me your glory", in Exodus 33:18? Or was Philip hoping that they would be caught up into heaven to see the Father? Something else?
Philip wanted to see The Father with his own eyes, just as he sees the Son of God with his own eyes (Son of God == Jesus). To put it another way, he wanted to see The Father in physical form.
The 2 previous verses gives us a clue as to what triggered Philip to ask this question.
verse 6: Philip's train of though might have been "If Jesus can show me the Father, then why not ask? This would clarify so many things for me."
verse 7: Philip's train of thought might have been "That's confusing. How have I seen the Father? But if Jesus is right, then I want to see the Father [again]".