Insufficient storage space

There are two unrelated answers. First. the space on the phone is in different units than the space in iphone specs. So a 16 GB phone is 16 GB in base 10. That SAME AMOUNT of space is measured in base 2, where 1K=1024 bytes. So it will be reported as 14.9 GB on the phone. It is still 16 GB, just expressed in different units. (See: How OS X and iOS report storage capacity - Apple Support for a detailed explanation).

The other reason is iOS takes space. About 2.5 GB in base 2 measurement. And storage formatting takes some space. The net result is that on a 16 GB phone the available space for apps and app data is about 11.7 GB, which isn't much. And its why Apple's smallest iPhone is now 32 GB.

To get a more detailed breakdown of what's taking up space on your iPhone, connect I to iTunes and the summary page will show you a breakdown by content. If the "other" section is more than a few megabytes, then you need to restore your phone to factory settings as this is mostly cached files, and iOS does not offer a way to clear cache. Same applies if documents and data is taking up a lot of space and you don't use numbers, pages, or keynote.

Your phone's not bad, but yes it does need to be restored to factory settings. Just make sure your contacts are syncing with iCloud or some other service before you restore it.