Like JW said, they are open to players of all ages, but most importantly, they are open to all skill levels also - which means they are the most competitive. Many professional level tour events have the name "Open" in them (French Open, US Open, Australian Open, etc) because they are "Open level" events - meaning anyone can enter the qualifying (or pre-qualifying) draws if they're willing to pay the entry fee. You will usually only see professional level players enter though, because most open divisions are full of very talented players.
Another reason why open divisions exist are because at the higher skill levels of the game they are fewer players available to put into a tournament draw so they have to combine the upper skill level players together to have enough. They are plenty of players generally at the 2.5-4.5 level, but at 5.0 and above there generally aren't enough 5.0, 5.5, 6.0, etc. to have a division or "draw" just for that specific skill level. With an "open" division, anyone above, say the 4.5 level can enter and generally expect to draw an opponent that is of similar skill level.
To answer the last part of your question - generally a tournament director doesn't know the rating level of a player in open divisions unless they have self-rated or already have a USTA rating - but most people at the lower rating level (like 2.5) know enough not to enter themselves into the open draw of a tournament. I have never been a tournament director (though I know some people that have) and they generally know the names of most players that enter their open division and know that they belong there.