The seeming paradox that a glass is at the same time a liquid and a solid is not easily reconciled. Glasses are "solids" produced by cooling a molten liquid fast enough that crystallization does not occur at the normal freezing point. Instead, the liquid supercools into the thermodynamic never-never land of metastability: kinetically settled enough to exist as a well-defined state of matter, yet not truly thermodynamically stable. As the supercooled liquid cools to lower and lower temperatures, the viscosity of the liquid increases dramatically. That happens because as thermal energy becomes ever less available, chemical bonds within the liquid constrain the atomic motion more and more.
As the glass cools, the time it needs to demonstrate liquid behavior (the "viscous relaxation time") increases and eventually reaches extremes. At the so-called glass transition temperature, the relaxation time is on the order of a few minutes. On a short timescale, the "liquid" glass will appear solid, but after a short while, it can be seen to be slowly flowing, like incredibly thick syrup. At still lower temperatures, the relaxation time reaches values that are truly geologic, i.e., many millions of years. Window glass at room temperature has a nearly incalculable relaxation time, approaching the age of the universe itself. For all practical observations, this glass is a solid. But its solidity is in the eye of the beholder.
(For more information about glass and glass making, see the Corning Glass Museum web site.)