Formula fields, summary fields, and lookup fields derive their values from the values of other fields. For instance, a formula field, C, might be the sum of the values in field A and field B. These source fields (A and B) are sub-fields of the calculated field C. A sub-field is any field that contributes its value to a calculated field.
It's not just the value of the calculated field that depends upon its sub-fields. Viewer access to the calculated result field also depends upon sub-field access permission settings. Again, say you've got a formula field C that sums values in field A and field B. The formula result field, C, inherits the most restrictive field permissions of all its sub-fields. This means that if a viewer can't see sub-field B, he can't see the result, C. So, whether or not any information shows in the calculated result field at all, depends upon the permission settings on its sub-fields too.
Often, you do want viewers to see the result, but not the contributing sub-fields. To accomplish this, remove sub-field permissions from the mix, by overriding them.
To override sub-field permissions:
Within the Permissions section, turn on the Override permissions of sub-fields checkbox.
Click Save.
Overriding sub-field access settings is, to some extent, a weakening of permissions. So when you enable this option, it displays in red.
Note: This feature WON'T override restrictions if:
You've restricted access to records and want the calculated field to show a summary or result of values in those records. This feature overrides field-level restrictions only, not record-level restrictions.
Sub-fields live in another application (and are part of a cross-application relationship).