A remortgage simply means to get a new mortgage, either with the same or a different provider. Mortgages are portable so you can move to different providers and this is a very common thing for people to do.
Most mortgages come with an introductory offer which can give you a lower interest rate for the first few years, but when this expires, you can often be put on a much higher standard variable rate (known as an SVR).
The majority of British homeowners automatically get moved onto their SVR, but do not realise that the savings could be enormous if they remortgage. In fact, the average UK household could save up to £4,000 on their annual mortgage payments if they got a better remortgage deal. A remortgage could come with much better terms and a new introductory offer that you can take advantage of.