What does it mean if you're connected to the Internet with limited access?

Simple Analogy : A garden hose connected to the spigot but the water is not turned on !

It’s like your phone is connected but you don’t have a number.
That’s VERY limited access.

A weak connection will give very low bandwidth, which means it will take ages to load web-pages, you won’t be able to stream music or video.

You are not connected to the internet. You have been recognized on the network but you have not been assigned a viable IP address.