What's the difference?
We are assuming that in this context the question is related to film, radio and television. In radio and TV, a series is a set of programmes of a particular kind which have the same title. These programmes can be drama (see also serial), comedy, factual, or documentary. Often there are a number of programmes made for a series, and then there can be a break of several weeks, months, or even years before another series is made. (In the USA, the word season is often used to describe more than one series made for television.)
For example, the British Naturalist David Attenborough has made several different television series on the natural world. John Cleese made only two series of Fawlty Towers and worked on three series of Monty Python’s Flying Circus (he was not involved in the fourth and final series). In movies, there can be a number of films that form a series such as Star Wars, James Bond, Indiana Jones, Toy Story, etc., even though these can be over a number of years; James Bond has been running for over fifty of them.
Now a serial is only related to radio and TV, and is mainly referred to a story – usually drama. These serials are broadcast on television or radio in a number of parts over a period of time, the end of each programme concluding in some form of a ‘cliff-hanger’ – that is, a moment of high drama where if you want to find out what happens next, you have to wait until the next episode. There are some serials that continue beyond that without any sign of concluding, usually continuing stories about the daily lives and problems of a group of people who live in a particular place. These particular examples are better known by their more derogatory term – soap operas.