It says I've reached today's limit. What does that mean?

Every plan, including membership, comes with a daily conversation allowance that refreshes each day, and members get a much larger one. A small counter shows what's left as you get close, and when you reach it your AI Friend lets you know in a friendly way. You can come back the next day, or upgrade for a larger daily allowance. (Call time has its own separate daily amount on top of this.)