AUC stands for the Area Under the Curve and usually refers to the area under the receiver operator characteristic (ROC) curve.
AUC stands for the Area Under the Curve. Technically, it can be used for the area under any number of curves that are used to measure the performance of a model, for example, it could be used for the area under a precision-recall curve. However, when not otherwise specified, AUC is almost always taken to mean the area under the Receiver Operating Characteristic (ROC) curve. The acronym AUROC is sometimes used to indicate this AUC with greater precision.
The curves for which the AUC might be calculated are usually plotted within a unit square. Thus, the maximum AUC would be $1$. Unless the underlying model is badly misspecified, the minimum AUC is typically $.5$. These analytical bounds help make the AUC interpretable.
A good place to start reading about ROC AUC is Tom Fawcett, "An Introduction to ROC Analysis."