In a computer's central processing unit (CPU), an accumulator is a register in which arithmetic and logic results are stored.
Without a register like an accumulator, it would be necessary to write the result of each calculation (addition, multiplication, shift, etc.) to main memory, perhaps only to be read right back again for use in the next operation. Access to main memory is slower than access to a register like the accumulator because the technology used for the large main memory is slower (but cheaper) than that used for a register. Early electronic computer systems were often split into two groups, those with accumulators and those without.
Modern computer systems often have multiple general purpose registers that operate as accumulators, and the term is no longer as common as it once was. However, a number of special-purpose processors still use a single accumulator for their work, in order to simplify their design.
Mathematical operations often take place in a stepwise fashion, using the results from one operation as the input to the next. For instance, a manual calculation of a worker's weekly payroll might look something like:
A computer program carrying out the same task would follow the same basic sequence of operations, although the values being looked up would all be stored in computer memory. In early computers the number of hours would likely be held on a punch card and the pay rate in some other form of memory, perhaps a magnetic drum. Once the multiplication is complete, the result needs to be placed somewhere. On a "drum machine" this would likely be back to the drum, an operation that takes considerable time. And then the very next operation has to read that value back in, which introduces another considerable delay.
Accumulators dramatically improve performance in systems like these by providing a scratchpad area where the results of one operation can be fed to the next one for little or no performance penalty. In the example above, the basic weekly pay would be calculated and placed in the accumulator, which could then immediately be used by the income tax calculation. This removes one save and one read operation from the sequence, operations that generally took tens to hundreds of times as long as the multiplication itself.