The main advantage of a Fixed Rate mortgage deal is that it protects you from any rise in Interest rates by having a fixed monthly payment for the duration of the deal.
Fixed Mortgage deals are usually available as;
1 year Fixed deals
2 year Fixed deals
3 year Fixed deals
5 year Fixed deals
and
10 year Fixed deals
They provide easier monthly budgeting and as mentioned provide you with peace of mind knowing that an increase in the Bank of England rate will not mean an increase in your mortgage. 
Fixed mortgage deals are also available as an interest only mortgage or as a repayment mortgage.