In simple terms, when you have a mortgage you’re committed to a specific plan to pay X per month over a certain period of time.
Remortgaging is moving to another plan where you can change that plan to pay Y per month instead over a different period of time.
When you move to that different plan, the new provider “buys” the remaining debt from the previous provider, and you can add to that debt if you want as part of the exchange, so you effectively have a bigger mortgage but have a lump sum for house renovations or whatever.
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