Do I pay off the entire mortgage?

I have just inherited some money (60k) which coincides nicely with the end of my £50k 5 yr fixed rate mortgage. I am going to therefore pay of my mortgage but just wondering if I should pay off the entire amount? I would like to move house in a couple of years and was wondering whether it would be easier if I kept a small amount in my mortgage? My mum keeps saying that I should but after researching I can't see why?

Many thanks