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.
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.
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.