If your gutters overflow during a heavy rain, either the gutters and/or downspouts are clogged, the gutters are sagging and thereby preventing water from reaching the downspouts, or the gutters and downspouts are not large enough to handle the volume of rain runoff.
In most cases, gutters overflow because leaves and debris are clogging them, essentially creating dams that prevent water from flowing to the outlets above the downspouts. In fact, these clogs often occur right at the outlets. When this is the case, it’s time to clean out the gutters. For more about this, see How to Clean Rain Gutters.
Gutters that sag are a different issue—and the more they fill up with water, the more likely they are to sag because they become so heavy when full. For more about this, see Rain Gutters Sag.
If the gutters overflow but are not sagging or clogged, you will probably need to install new, larger downspouts and gutters.