To open next it says visit storage what does that mean?

That means you need more flowers to reach the next level and you have enough items in storage to meet that flower goal. However, if you lack the island space to bring out the items, you will have to gain flowers in one of the following ways: buy decoration, renovate landscape, upgrade 3x3 buildings, get through Jack's delivery. If you buy decoration, you'll have to wait until construction is complete and you remove the red ribbon before the flowers will count.