In order to preserve freshness, biscuits need to be packaged appropriately for either storing or presenting as gifts. In order to keep them as moist as possible you will want to protect the biscuits from contact with air. The best packaging options for biscuits prevent air penetration yet still make for a nice visual presentation.
This is probably the most traditional way of packaging biscuits. Place the biscuits on a plate (paper if you plan on giving them away as gifts). Once they are on the plate, wrap them in cling film. The biscuits will only stay soft for about two days this way.
Plastic baggies do a better job of keeping air out of freshly baked biscuits than simple cling film. The downside to this method, however, is that you lose some of the presentation value if giving them away. The upside is that the biscuits stay softer and fresher for several days.
Baked Goods Box
Cookies, pies, and similar baked goods are often gifted in baking boxes. However, biscuits don't take well to being exposed to that much air. In order to keep biscuits moist, they need to be protected from exposure as much as possible. However, baked goods boxes do provide some opportunity for creatively presenting biscuits as a gift so, if you choose this method, place the biscuits in some other type of packaging within the box (such as cling film as mentioned above).