A remortgage is when you switch your mortgage for another one on the same house. As simple as that.
It’s not when you move house, it’s simply to refinance the same house.
Remortgaging is very common and highly recommended, as most mortgage deals have an introductory period during the first few years of the mortgage with a fixed low rate, often called a fixed rate period.
After this introductory period ends, you would normally move onto a standard variable rate, which is typically higher than the initial rate, and so you would remortgage to a new deal to get a better rate (the lower introductory rate on a new mortgage).
And the cycle would repeat until you pay off the mortgage completely.
You can also remortgage to release cash (equity), in your home too, and for whatever reason you like, often for home improvements. This would involve remortgaging to a new deal with a higher loan-to-value, meaning you have less equity in the house, and the lender would give you the difference in cash.