I've been recently told that it's hard to identify messages whil esearching because of the conversation.
This tiop helps you to get only the right messages displayed.
Generally, one searches messages using the from:email operator.
This returns messages that have been sent from the given person, but the ones sent to me and the one I was in cc:
Adding the to:me or the cc:me operator helps you refining to the ones sent to you directly (to:me) or where you were only in copy of the email (cc:me)
THen, when you open the conversation in the search list, only the messages matching the rule are expanded by default.