What is dimensional security?
Dimensional security is when you want to use a security rule to filter the data in the cube based on a dimension. A very typical example would be if you wanted a salesperson to see just the data from their sales territory.
Analysis Services has Role Based security
Analysis Services uses "role based" secuirty. This means that a role contains members and then the definition of what those members can access. As you can imagine, this can cause a problem if you have a very granular data restriction requirement. If I was a retailer with 500 stores, I would NOT want to create 500 roles, one for each store, where I assigned the user and the corresponding store. This would be a maintenance nightmare.
What is table driven dynamic security?
Table driven security is where you drive the individuals security off of the data in a relational table. This approach is much easier to maintain because now there in only one role and the data in the table is what is driving the dimensional filtering. This can easily be implemented by creating a table which has the user's network login id and the dimension member that they have access to. This approach is flexible in that a user can see multiple members.
This is not overly difficult to set up and could easily be done during a remote session.