"We're not ready for the next step yet" is just a simpler way of saying "We're happy where this relationship is right now but we're not ready for a deeper level of commitment". There aren't actually any "steps" it's just an easier way of explaining their relationship.
I love my boyfriend and we plan to be together for the rest of our lives but I wouldn't have moved in together after our first date because we weren't ready. I could also say we weren't ready to take that step and it means exactly the same thing