A byte stream is an abstraction which describes a particular kind of communication channel between two entities. (In computer networking the term octet stream is sometimes used to refer to the same thing; at the time the concept was first used in the field, not all computers used 8-bit bytes, whereas on most modern computers bytes are octets.)
Formally, it is a channel (often bi-directional, but sometimes uni-directional) down which one entity can send a sequence of bytes to the entity on the other end. In almost all instances, the channel has the property that it is reliable; i.e. the exact same bytes emerge, in the exact same order, at the other end.
Less formally, one can think of it as a conduit between the two entities; one entity can insert bytes into the conduit, and the other entity then receives them.
The pipe mechanism used in a number of operating systems, such as Unix and MS-DOS, is a uni-directional byte stream. One well-known example of a communication protocol which provides a byte-stream service to its clients is the Transmission Control Protocol of the Internet protocol suite, which provides a bidirectional 8-bit byte stream; it is being used to bring you this Web page.