That's a great question Danimal2485, and just earlier today I was mentioning over at /r/arthistory that this was my favourite work of art. When I saw your post though I was just running out the door so I made a discussion about it over at /r/arthistory to see if anyone there had any input, and a number of people chimed in.

The painting is unique in that you are looking at a scene that Diego Velazquez is painting, and yet you can see him within the painting as an artist - so this immediately turns the traditional idea of the gaze on it's head. You are not the one doing the active gazing at an artwork, you are actually the subject of the painting as Velazquez is looking towards you. You can't see the portrait of yourself on the easel, but you can see the reflection of yourself in the mirror at the very back, you are the King and Queen of Spain.

And yet this painting is also about the little Infanta Margaret Theresa, who takes a very central position to the painting. I think what really stands out is that each character is engaged in something different that has a different meaning, and their presence signifies various things as well. The wikipedia article actually does a great job of laying this out in the "Subject Matter" section where it outlines each person and their meaning.

As others have pointed out in the /r/arthistory thread, Foucault writes in the first chapter of "The Order of Things" an in depth analysis of the work that is worth reading, though a little hard to get through, but it talks about this idea of the gaze further.

There's another article on the piece which comes from an anthropological angle called "The Mirrors of Las Meninas: Cochineal, Silver, and Clay" by Byron Ellsworth Hamann which is particularly interesting as it dissects other aspects that are traditionally overlooked and ties them to the colonial history of Spain. So one being the cohineal dye used to colour the drapes was collected by slaves in Central America in the 15th century and became a large export during the colonial period. This adds another level to the work as there is an obvious social hierarchy between the subjects, but these individuals are also involved in and implicit in a large colonial expansion into the Americas at this period, resulting in great wealth for Spain (at the expense of others). These are just a few of many, many different ways to look at it, and it's a work that's always prompting new examinations.

It also is much more impressive seeing it in person on the walls of the Prado museum due to it's sheer size dominating over you. Actually being there in front of it really helps you to understand this feeling of being out of place as a viewer, and implicit within the painting.