First version
Seven entrances or seven doors are a reference to the mystical plexuses or lotuses of yoga - the muldhara, svadhisthana, manipura, anahata, visuddha, ajna, and sahasrara. It is only after one has gone through each one of these lotuses that the Lord is seen.
Second version
There are 14 "Lokas" or universes mentioned in Hindu scriptures. 6 are below or on one side of the universe we live in and 7 are above or on the other side. The 7 universes above are referred to as Bhu:, Bhuva: Suva: Maha: Jana: Thapa: and Satya Loka. This is there in Gayatri Mantra too. Each door opens to an universe. When you pass through each of the universe above, after passing through the 7th door, you reach Satya Loka or the Brahman or Lord Vishnu. I think that is the significance of going through the Sapta Dwara to get the Darshan of Lord Vishnu.
