Think of it like a spring / fall cleaning, when you de-clutter and start fresh, and give it more room to function by deleting years-old photos and apps.
Imagine opening iTunes and seeing this, so beautiful…
1 – Backup – photos / contacts / calendar / notes
2 – General > Reset > Erase All Content and Settings
3 – Enter passcode and follow instructions
4 – For sure you’re backed up right
5 – Click Erase
6 – Re-install apps
7 – Use the opportunity to change all your passwords (or at least – bank / email / Facebook)
8 – Done.
When the phone is now behaving like new, you’ll be all, “why was I putting up with that lag all this time…”