You would need to change or create a new APN if you were to change your Mobile Network Provider or sometimes if your change your SIM Plan on the same Network.
EE tend to use the same APN for all there SIM Plan types "everywhere" but for example Vodafone use different APNs for PAYG, Contract and Mobile Broadband.
APNs are part of a International Data Gateway Address which were developed within GSM 2G era for 2.5G GPRS, idea then was to introduce an Always On (Always Connected) Data connection to a Packet Switched Network rather than send Fax or Data over a Voice Network, so effectively ISDN for the Mobile Network. APN is also used as an Identifier which was important part of using Data whilst Roaming Abroad on different Networks.
In the early days, GPRS Mobile Data was designed to connect to all sorts of Stuff, other ISDNs, Different Data Networks, Banks, Finiancial, Secure Servers etc or just another GPRS Mobile on the other side of the Planet, but as it's mainly used for normal Internet Access now, most Phone Manafactures just put Global Settings in the Phones Firmware now which should in theory Auto configure your APN Settings for you when you insert your Network SIM.
Probably also worth pointing out that whilst you shouldn't need to change your APN Settings or a Routers Profile that contains the APN Settings you probably won't be able to if the Device is Network Locked or Network Firmware Restricted.
