A transmission line is the term used for how a conductor looks to high-frequency AC signals. Unlike low frequency signals, where a conductor functions more or less on a 'what goes in at one end comes out the other end exactly the same' way, the behaviour at high frequencies is considerably more complex. The term 'tranmission line' is used to cover this behaviour.
Without going into the theory (which is fairly complex), the behaviour of sound in a pipe provides a very good analogy. Imagine sending a sound down a pipe: places where the shape of the pipe changes can cause an echo as some of the sound energy is reflected back down the pipe in the direction from which it came; e.g. if the pipe switches from a large diameter to a small, there will be an echo off the edge. Reflection is the term is used for the analogous behaviour in transmission lines.
If the end of the pipe is a blank flat cap, it will produce a strong echo (reflection) when the sound reaches it; but if something to absorb the sound energy (such as a a wad of cotton) is placed there, there is no echo. The name for the analogous device in a transmission line is a terminator.
If a transmission line branches, some of the energy will travel down each branch, and unless each branch is properly terminated, it will produce reflections which travel back the way the signal came.
In computers, busses, especially longer ones, are transmission lines, and so need to have termination at each end to prevent reflections. For high-speed circuitry (such as ECL), all inter-chip connections need to be handled as transmission lines.