Hi,
There are two common ways to handle this:

1) Have the solar panels charge batteries, and use the batteries for rainy day power. You have to have enough solar panels and batteries to collect enough power on sunny days to get you through the rainy days.

2) Some houses with solar panels tie into the utility power grid. In this case, the power for a rainy day comes from the power grid. Anytime the panels are not generating enough power, the grid supplies the extra. Anytime the solar panels are generating more power than the house can use, the excess goes out to the grid, and your electric meter "turns backwards" to give you credit for the power.

Gary