You got that message because you don't have enough storage capacity left in your vault to hold the items your dweller is bringing back from the field.
In this situation, you have two options:
Increase storage of your vault by building more storage rooms and/or by upgrading any existing storage rooms you already have.
Sell some of the items the dweller brought to you before you bring them back into the vault.
To determine how much more storage capacity you need, just click the dweller who has returned and look at the items they are carrying. The items with a red badge (background color) are the items that won't fit into the vault. The ones with a green badge will fit in the vault (see picture below).
As you buy more storage, you'll notice that more items will turn green. Once all items are green, you can hit the collect button and bring your dweller and all the items they are carrying inside the vault.
Although you can bring all the items inside your vault, you don't have to. You can also sell some less valuable items before the dweller gets in. You can select items for sale by clicking on them. Once you click on an item, they will turn into their value in caps. You'll also notice that more items turn green as you select them for sale. See picture below. You can revert the selection by clicking on them again.
I had exactly the same problem the first time I got a dweller back from a long trip: bought 3 storage rooms to fit all the stuff. That's probably because it's not very intuitive that you can sell the items before you tap one of them. But the extra storage ended up being useful anyway.