In other words, chances are that you simply misplaced the messages, moving them to another label by mistake. If that’s the case, finding them shouldn’t be too difficult. (Remember that in Gmail, a label acts much like a folder in other programs, except that you can assign multiple labels to any message or conversation. See How to manage Gmail labels for details.)
To find a lost message, search for a word or words that will be in that message, and hopefully not in too many others. The search results are sorted by date, so finding the right one shouldn’t be too difficult.
But if you can’t find the message, look at the bottom of the list. If you see the words “Deleted messages match your search,” click the View them link.
If that doesn’t work, check your Spam section.
Of course, it’s possible that you could have deleted them for good, in one of the three ways I describe above. Those accidents may not be likely, but they’re certainly possible.
In that case, you may have no alternative except contacting the person who sent you the email (or who you sent it to) and ask for a copy.