what is an APN ?

An APN is an access point name, so I think your request is whether it's OK for your iPhone 4 not to be connected to WiFi.

The answer is yes.

But if you don't connect to WiFi, it means you will rely on your cellular carrier to get you the data you need (e.g., internet access). This may cost you.

Access Point Name. It defines the network you can connect to for data with your carrier. If you are required to have this and don't use it you you won't be able to use cellular data. (See http://mobileoffice.about.com/od/glossary/g/APN.htm.)