Crm security privileges Append, Append to, Assign

Append - To control the lookup fields of the other entities on the form of this entity

Append to - To control the lookup field of this entity on the forms of other entities

Assign - To control the Owner field of this entity.

Here is a good reference for this topic. http://community.dynamics.com/product/crm/crmtechnical/b/crminogic/archive/2010/05/03/append-v-47-s-append-to.aspx