Saying that ice is slippery is like saying that water is wet -- it's something we've known for as long as we can be said to have known anything. Presumably, humans as a species knew ice was slippery before we knew fire was hot, or that it existed. But ask anyone why, and they won't be able to give you any better explanation than one of those cave people would have.
Apparently this is a simple question with a not-so-simple answer.
I believe the general consensus is that there is a thin layer of liquid water on the surface of the ice. This thin layer and the solid ice below it are responsible for the slipperiness of ice; the water easily moves on the ice. (Well, why is that? Perhaps another SE question.)
However, this is no real agreement as to why there is a thin layer of liquid water on the surface of ice to begin with. See here for a 2006 NYT article. And if are interested in the actual physics paper that the news article is based on, see here (DOI).
One idea states that the molecules on the surface of ice vibrate more than the inner molecules, and that this is an intrinsic property of water ice. Since the outer molecules are vibrating faster, they're more likely to be in a liquid state.
Another idea is that the movement of an object over ice causes heating, though I found conflicting sources as to whether there's a consensus on this.
There is a popular idea that many hold but doesn't appear to hold water. (Heh.) This idea posited that the added pressure on the ice from a foot or skate causes the melting point to rise, which would cause the thin layer of liquid to form. However, calculating the resulting pressure and increase in melting point doesn't line up with observation; the melting point certainly does rise, but not enough.
All the ice we see around us in nature is not far off from the melting point of the ice - this gives a reasonable probability that there will be monolayers of water on top of the ice surface. Additional energy input by friction would cause more ice to melt on the surface, thus giving it a slippery property. Ice near absolute zero temperature (i.e. much below its melting point) would not be slippery.
There are a couple of reasons: the surface properties of the ice, and the formation of a thin layer of liquid water.
First, ice tends to have a relatively smooth surface, due to the interaction of water molecules forming a regular, crystalline structure (that's what ice is, after all). Gravity helps: it pulls the surface molecules down, so they all tend to be at the some level, making for a very even surface and very low coefficients of friction.
Second, there is the liquid water on the surface. This happens for two reasons:
First, at anything above absolute zero there will always be a little bit of water that is transitioning back and forth from solid to liquid (melting) and/or gas (sublimation). Molecules deep in the ice are surrounded by other molecules that are nearly stationary, so those molecules are unlikely to move. Molecules on the surface, on the other hand, are less tightly bonded to their neighbors, because they don't have neighbors on all sides, so they can "pop loose" more easily and move around in water or gas phases.
Second, pressure melts water ice. Water is one of very few compounds that is less dense in solid form than as a liquid. This is why ice floats in water. The act of applying pressure -- say, by standing on a sheet of ice -- compresses and actually melts a bit of the ice. If you've ever seen anyone cutting ice with a wire, this is how it works: the pressure of the wire actually melts through the ice, if the pressure is great enough.
So, if you stand on ice, you will melt a very thin layer of it. Add that melt to the spontaneous melting and refreezing of the topmost layer of water molecules and the fact that you are already on a smooth surface, and things get very slippery, very fast.
Ice is the solid form of water. Under pressure, depending on the local temp and how much pressure is applies, ice changes state into liquid water. The more resistance a surface offers to objects moving across it, the less slippery it is.
Say you put on ice skates, and skate. the blades exert enough pressure to melt the ice beneath the skates to form water, a surface with very little resistance , and he layer of water acts as a lubricant between blade and the ice below.
On another day, it is too cold or the skater is too little t exert enough pressure and the footing is good.
I suggest people always knew that ice might be slippery and pay extreme attention to details locally to decide if this ice is slippery