Å besøke is a verb, it means to visit somebody. 'Jeg skal besøke min søster i morgen' means 'I am going to see (or visit) my sister tomorrow.''Et besøk' is a noun, it does not mean the person who comes to see you but more the fact that someone comes to see you. If someone says 'Det var et langt besøk' he means the guests stayed a long time.
' Jeg dro for å besøke min mor i går, men det ble et kort besøk for hun var i dårlig humør' means' I went to see my mother yesterday, but it was a short visit because she was in a bad mood.'