To make it quicker and easier to follow a conversation, FastMail groups replies with the original message. This means you can see all the related messages together, rather than having them randomly scattered across your Inbox, Sent and other folders.
Most actions with conversations should feel fairly intuitive. However, there are some aspects that might need further explanation, particularly if you are used to a non-conversation workflow.
Default behaviour is to reply to all members of a conversation when responding to a message. This can be changed in the Settings → Mail Preferences screen in the Writing section. Change from "Reply to everyone in the conversation" to "Just reply to the sender".
When you delete a conversation (by selecting one or more conversations in the mailbox then clicking "Delete", or by opening a conversation and clicking "Delete"), you are deleting ALL the messages in that conversation across ALL FOLDERS, not just the message you see in the mailbox, even if some of those messages were received long ago.
Note that this includes messages in your Sent folder that are part of the conversation as well.
You can change the delete behaviour to only delete messages from the currently selected folder when deleting a conversation in the Settings → Mail Preferences screen. In the Reading section, toggle the Delete grouped messages from all folders setting. When set to off, deleting will only delete messages in the current folder, not the whole conversation. This is what Apple's mail clients do when deleting conversations; the default (deleting the whole conversation across all folders) is how Gmail behaves when deleting conversations.
To delete a single message from a conversation, open the conversation and click the "More" button in the header of the message you wish to delete. Then click "Delete".
If you prefer to deal with every message separately, you can turn off conversations. Each message will be treated completely independently.