A con report is a first-hand recounting, typically first-person fanwriting, of what happened at a convention. They were once printed in fanzines but now often posted to the internet or e-mailed.
Most often, conreps are anecdotal, their intent to entertain rather than provide information, so they rarely aim to tell you about every item on the program, just the ones the writer attended, if any, and what the writer and others said and did. A well-known trope is the report that spends more time on the writer's trip to the con, than on describing the event.
Sometimes the stories told are apocryphal, and one fanwriter's account of an incident may vary from the next, so they should not necessarily be taken as gospel. After all, during the event itself, fans tend to consume intoxicating substances and get too little sleep, so their memories may not be accurate.
Then, too, the best fanwriters are apt not to let the truth get in the way of a good story, and some con reports may be considered a form of faan fiction. The "...and then I did" diary-style report can be deadly dull. It's considered good form to write more about other people and events than about yourself.
Controversial events may be reported from only one side. Harry Warner, Jr.'s fanhistories were criticized by contemporaries because he took literally what was recorded in fanzine accounts and rarely checked them against other fans' memories.
A con report is typically the centerpiece of a fan fund winner's trip report. Con reports proliferated with the explosion of cons in the 1970s, and there was some minor controversy amid fanzine fans about zines filled mainly with conreps. Jackie Causgrove's Dilemma was one of the best of these.
On the internet, Evelyn C. Leeper (who has been nominated for multiple Best Fan Writer Hugos) is one of the better examples of those who emphasize the "report" in that she generally provides detailed notes on panel discussions, telling without interpolation who said what and reporting the back-and-forth discussions that generally ensue. During the days when she was reporting for Uncle Dick's, Leah Zeldes, a journalist by trade, took extensive notes at conventions, particularly WSFS business meetings, but this is rare.
See Fan Memoirs.