In layman's terms, "Cellular data" is the
internet, accessed through your network provider.
If you turn that off, you won't be able to access features or services that rely on the internet such as email, web browsing, push notifications or anything that connects to the internet. However, if you have wifi on then of course you'll be connected to the internet. Turning off "Cellular Data" just prevents your phone using data(internet) over your network provider - ideal if you have a capped data allowance or fear being charged for use beyond your allowance by your network provider.
As phone calls and SMS do not rely on the internet, they'll work fine. If you want to block calls and SMS, turn on "Airplane mode" as this will disconnect your phone to your network provider (including the internet). If you wish to access the internet, turn on wifi. Alternatively, use the "Do Not Disturb" feature in iOS.
Hope that simplified it