Since soft contacts are made of polymer that absorbs water it is only natural that if you leave your contacts to dry (e.g. prolonged use w/o lubrication) it will stick to wherever or whatever will give it moisture in order to remain soft and flexible w/c can be unfortunate if it is your eyeball.
Posterior to Iris
Where your iris and pupil are on your eye, there is a slight round bump, as shown in this picture: http://www.retinaaustralia.com.au/images/eye6.gif A contact lens is shaped precisely to the size and shape of that bump, so that when you place a contact lens in your eye, the contact lens tries to find the place that it fits around perfectly, which is over your pupil and iris.
The iris surrounds the lens.
The iris acts like the aperture of a camera lens.
My dad is an eye doctor and the same thing happened to me... you should just wash it out well with your lens solution and it'll be fine.
Anterior
The colored part of the eye is the Iris.
iris and ciliary muscle
iris
Lens does not belong, as it is not part of the structures involved in the formation or regulation of the aqueous humor within the eye like the ciliary body, iris, and suspensory ligaments.
The colored part of the eye is called the iris. The black dot in the middle is the pupil which is covered by the lens.
Your contact lens will stick to the "least wet" thing it is in contact with. Try putting a couple of drops of solution on your finger so that the lens can easily move off your finger onto your eyeball. The easiest way that I find to put a lens in is to place it on the eyeball and then slowly move your eye (ie look away). Because of the shape of the lens, it moves with the eyeball and "off" your finger.