I think everyone will have their own opinion, as one man's fully finished profile will be another who says it's only just begun. For me:
1) Clear, well-written biography that is fact-based, but has some entertaining language that paints the picture of what happened, during what time period, and relates to to historical references of the time and to the events of that person's life. It should also be easy to follow and not jump around, but take you from birth to death and have some foundation in genealogical research (and not just a copy of Wikipedia, for example).
2) A tasteful background that's clean and not animated nor overly detailed. Too much in this case can quickly become... too much.
3) Pictures that support the profile, to include the individual (2-3 at most - more than this tends to lean towards overkill), possibly a photo of their gravesite, and possibly a photo of some key event in their life. Generic photos are OK, but I usually don't care much for them. Showing a "Conestoga Wagon" photo of a museum piece to denote someone who made a wagon trail is OK but not really necessary. Although showing a drawing from the period of the same thing helps draw me back to that time period, so it can be done right.
4) Lastly, templates and categories that support the profile.
So I exceeded the 2-3 - oh well... had to fit that last one in.