Degree is a mathematical property of a curve or of a surface dimension that controls how many CVs are available for modeling.
The number of CVs for each curve span is controlled by the degree of the curve. The default curve type in Alias is degree 3, which has four CVs for the first curve span.
You can choose to have fewer CVs per span, or, if you have an advanced version of Alias, you can create curves with more than four CVs per span.
The degree of your curves can affect data transfer to CAD packages. Some other packages cannot accept curves with degree higher than 3.
Surfaces can have different degrees across their width and length. So, for example, a surface could be degree 3 along its width, and degree 5 along its length.