Upa means close and vasa means residence and Upavasa simply means that when you are close to God, all your bad qualities will be removed and you will attain good qualities. (SSB 1974 Part II, p. 69)
Upavasa is to live close by. Upasana is to sit close by. We do not feel the heat when we are sitting near an air-conditioner. Likewise in winter if we sit near a heater, we get the benefit of warmth. We do Upavasa because we want to go close to God and stay near Him.
What is the benefit of going close to God? The benefit is that the sat-cit-ananda of God will come to us and the bad qualities in us will go away. This is how we should understand the meaning of Upavasa. It is our attempt to go close to God but in practice we have reduced this to eating half a dozen chapattis, a dozen plantains and drinking a pint of milk after refraining from eating rice. Is there any meaning in this kind of Upavasa? Often, in this manner, we are not comprehending the correct meaning of our sacred culture. To some extent, we are therefore disappointed at the results which our sadhanas and practices bring us. (SSB 1973, pp. 266-267)