This refers to the number of new people who clicked Like and became fans of your page during the selected time period. This does not take into account the number of fans you lost during the period (Lost Fans).
In the example above, the page gained 145 new fans during the month of December.
This refers to the change in the page's number of total fans during the selected time period. Therefore, it takes into account the number of New Fans as well as the number of Lost Fans.
In the example above, the page gained 17 unique fans during the month of December.
Note: In theory, the number of Unique Fans gained should equal "New Fans minus Lost Fans". However, this is rarely the case; Facebook regularly adjusts the total audience (for example, when deactivating invalid/inactive Likes) which gets reflected in the total audience, but not in the number of New Fans or Lost Fans.