If you are currently on Exchange Server, you most likely are using Public Folders in some sort or shape. Maybe you are considering Exhange Online in Office 365, and heard somewhere that Exchange Online does not support public folders?
Well, thats true.
The good thing is, many of the usage scenarios usually found in public folder solutions can be imitated in Office 365. The trick is analyzing how you are using public folders today and then imitate that in Office 365. Some of the common public folder scenarios are:
Based on the analysis you will imitate your public folder workloads using primarily Shared Mailboxes in Exchange Online and/or Document Libraries or custom lists in SharePoint Online.
E.g the calendar part in the first bullet above can be accomplished in two ways:
You can read much more about building an environment that mirrors your use of public folders in Exhange in the whitepaper "Migrate from Exchange Public Folders to Microsoft Office 365" - link