I think it depends on what is going on. There are lots of things that can cause leg weakness, right down to vitamin deficiencies.

In the case of MS as well as other neurological conditions, from what I understand and in addition to Erins explanation, nerves are telling our muscles to contract when they really don't need to contract, otherwise known as spasticity. This constant contracting can certainly makes us feel as though we have run a marathon when all we did is walk 25 feet (sometimes less). Our muscles get tired much quicker and we have to use more effort and energy to get our bodies to move in the way we want them to, such as walking. This causes muscle fatigue that you are describing.