Use these options to set what happens when you select Mesh Display > Average.
Turn this option on so that all the normals in the calculation have a length of 1, and each one contributes equally to the average. This is the default setting.
If this option is turned off, and if you explicitly set normals where the length is not equal to 1, then the contribution of these normals to the average is weighted by the length of the normal (the new normal will be closer in direction to the longer normals).
If Normalize before averaging is off, you can keep the length of the normal that resulted from the calculation, or set the length to 1 by turning on Normalize after averaging. The length may be significant in future invocations of Average Normals. If Normalize before averaging is on, this option is disabled, since the result will be automatically normalized.
Turn on Do not normalize when you do not want the normals to be normalized before averaging.
The vertices within the distance you specify are considered as a group to share a normal which is the average of the normals in the group. So your selected vertices may be divided into several groups, and each group averaged separately.
If two normals of exactly opposite direction are averaged, the result will be a zero-length normal. While this is valid in Maya, it may not be what you want. If this option is turned off, the normals are replaced by user-specified value (see below).
If Allow Zero Normals is on, this option is disabled. If Allow Zero Normals is off, the normals are replaced by the X, Y, and Z values you specify here.