"Corked" wine refers to wine that has been exposed to cork taint - the presence of a chemical compound called TCA (or trichloroanisole). TCA is formed when natural fungi (of which many reside in cork) come in contact with certain chlorides found in bleaches and other winery sanitation products. If a winery uses corks infected with this fungi, the wine becomes tainted.
While unpleasant to taste, cork taint is not in any way harmful to drink. Most consumers don't even realize their wines have a mild case of cork taint unless pointed out by a professional - Corked wines smell and taste of damp, soggy, wet, or rotten cardboard, in varying degrees. Cork taint dulls the fruit in a wine, renders it lackluster, and cuts the finish. The obviousness of the corked smell and taste depends both on the extent of the taint, as well as the wine drinker’s sensitivity to it.