A bus in a computer is synonymous to a pathway that the electrical signal takes to get from one component to another.
It is basically collection of wires through which data is transmitted from one part of a computer to another. You can think of a bus as a highway on which data travels within a computer. When used in reference to personal computers, the term bus usually refers to internal bus. This is a bus that connects all the internal computer components to the CPU and main memory. There's also an expansion bus that enables expansion boards to access the CPU and memory.
All buses consist of two parts -- an address bus and a data bus. The data bus transfers actual data whereas the address bus transfers information about where the data should go.
The size of a bus, known as its width, is important because it determines how much data can be transmitted at one time. For example, a 16-bit bus can transmit 16 bits of data, whereas a 32-bit bus can transmit 32 bits of data.
Every bus has a clock speed measured in MHz. A fast bus allows data to be transferred faster, which makes applications run faster. On PCs, the old ISA bus is being replaced by faster buses such as PCI.
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