The flexible mortgage is a relatively new type of mortgage. They are flexible as you can overpay your mortgage when finances allow (pay rise, bonus, an inheritance etc.) and then providing you have made overpayments in the past you can underpay or borrow back your overpayments when finances are tight (job loss, change in circumstance etc).
By way of example, if you overpay your loan by £100 per month for five years on a flexible mortgage the amount accumulated is made available as a cash reserve for you to draw on at any time during the remainder of the mortgage term. You will also have paid less interest during this time leading to more capital being repaid and effectively earning you tax free interest on the savings at the mortgage rate you are paying.
This cash reserve can be used for anything you choose including taking payment holidays, actual holidays or making a large purchase such as a car etc. Some lenders will issue you with a cheque book and encourage you to use the account as a bank account. However the amount you can withdraw is limited by the original sum of the loan.
An offset mortgage is similar except normally this will offset the value of a different account such as your current account against the mortgage liability. This is useful if you have regular, very large deposits of capital sitting in a savings account as you are effectively earning mortgage interest (tax free) rates on your savings and retain access to your capital as needed.
The down side is that flexible mortgages are normally more expensive than their non-flexible cousins so there may be little advantage to you unless you have significant capital deposits that can be offset against the loan.
Your home may be repossessed if you do not keep up repayments on your mortgage.