iOS7 requires additional space and if your iPhone doesn’t have enough storage, you will need to make room before this new iOS version will download properly. The easiest thing to do is to empty the cache and you can do that by going to Settings and then Usage. If you still don’t have enough space you might need to get rid of other data too though.
Videos and images take up an enormous amount of space and if you export them to your computer or some other device to save them in order to get them off your iPhone you can free up quite a significant amount of space. Apps would be the next thing to uninstall and ones you don’t use would be the first ones to get rid of. After you have removed everything that you no longer need you should have plenty of storage to update to iOS7.