Hi Oona;
Two different things to solve.
First is - Demos. A demo is not the full product. It is only a sample. It will frequently have part of the texture missing, or will have the word DEMO printed on it directly or hovering above it. That is so that people don't try to just wear the sample. Demos usually cost nothing or 1 Linden. The full product might cost a lot more than that.
The purpose of a Demo is to try the product and make sure it fits and that you like how it looks.
Second - How to open boxes.
Some things are already opened or unpacked when you buy or are given the items. Some are still in boxes. Since some items LOOK like boxes in your inventory sometimes the only way to know is to try to wear it, or to open it.
To open a box - Open Inventory. Drag the box from Inventory to the ground near your avatar. Right-click on the box, and choose Open. Then, choose Copy to Inventory. Everything will unpack into your Inventory where it can later be chosen and worn.
Once you've done that, right-click the box again, and choose Take. That will pick up the box, and avoid littering.

Now all that is only possible if the land owner allows things to be opened there. If not, then the box might pop onto your avatar. The box will also do that, cling to your avatar, if you right-click it in Inventory and choose Wear.
To remove things you don't want:
Open Inventory. Type WORN. Now anything you are wearing will be in bold letters. Anything extra, right-click the name of it in Inventory, and choose Detach or Remove. (You might wanna do that somewhere private)
How to wear things you do want:
Open Inventory. Type a keyword or find the item. It might be under Clothing or it might be below the trash can in its own folder. Find it, and right-click its name and choose Wear.
If you wear a dress in Second Life make sure to wear the little pants that go under it. Those will frequently be labeled "glitch pants." It will be in the same folder as the dress or skirt. If you forget those, you will feel a breeze as you walk around SL and also will give passersby a free show.
So, for now, remove the box and the demo with the above instructions. Oh, and if it's a skin you want to change, you don't remove those - you just put a new one on top of it.
Be sure to wear a bald cap under any 'prim hair' (the hair that looks like wigs) so it flattens your old hair and doesn't look like you are wearing two sets of hair.
Any questions?