With Pulse SMS, you can get better organization over your conversations by placing them in folders. Each conversation can be placed in one specific folder.
You can create folders by going to the "Manage folders..." option within the Android app's navigation drawer/side menu.
To put conversations into a folder, you have two options. You can go to that conversation's settings and access the folder from there through the "Select Folder for Conversation" option. Alternatively, you can move conversations in bulk by going to the "Manage folders..." section of the app.
You can add as many conversations to a folder as you want, however, each conversation can only be in one folder. Moreover, folders are meant for organizing conversations and not individual messages.
Folders do not affect what is displayed on the normal Conversation list. They are simply extra functionality/filters on top of the normal list.
Private conversations cannot be placed in folders.
Folders are accessible on the web interface as well.