The phrase budget at completion (often referred to as BAC) refers to the sum of all budget values that have been previously established for the work to be performed on a project, or on components within a project such as a schedule activity or work breakdown structure component. The budget at completion also can be referred to as the total planned value of the project. An easy way to loon at it is as follows. When each specific item of a project is documented, each of these items, components, activities, etc. is assigned a cost. The amount that it is expected to cost to complete that particular item. Then, each of these items can ad should be added up to determine the final budget on completion, which can then be weighed against the pre-determined budget for the project to help figure out if anything may need to be cut (in cases where the project may project to be over-budget) or if anything can potentially be added (in cases, albeit rare, in which the project may be coming in under budget).
This term is defined in the 3rd and the 4th edition of the PMBOK.