Gmail's conversations and labels features drives me crazy and I'm sure a lot of folks don't truly understand what is going on. Basically, if you email your friend, they reply, you reply, etc. etc., Gmail handles ALL of the emails as one thing called a “conversation” which can be multiple related emails. You can see this in the Sent Mail folder. If you replied to an email, you will see only one entry in Sent Mail and it will have all of the emails in the conversation.
So what's the big deal? Well, if you delete, say, the last reply you receive, all of the individual emails that make up the conversation are are deleted! This includes the initial email that you sent. Is that what you would expect to happen? Me neither.
Now if you wanted to save the initially sent email, what you have to do is expand that portion of the last email and choose Delete this message from the pop-up menu in the upper-right corner, next to where it says Reply. This actually deletes this individual email as well as any of the emails that follow this one in the conversation.
If you want to save the entire conversation in the Sent Mail folder(?), you have to just archive it, but apply no label. Sent Mail and Trash seem to be the sole exceptions to the Gmail labeling scheme. It's as if they had labels for Sent Mail or Trash, but they never appear as labels. Your only clue is that they appear in those folders.
If you want to maintain a record of everything you send, NEVER delete a conversation. Always archive those. I suppose a more workable practice is to only delete (solo) original emails you receive. If anything is part of a conversation, archive, well unless you don't want any record of any part of it.