Taking bird photos on an overcast day can be a little tricky because you may not have as much light to work with. On the other hand, there can also be a few advantages.
Natural light on a cloudy day tends to be cooler, so it can really bring out rich greens and blues. This can be especially good for photos that include foliage. Cloudy conditions are essentially the opposite of the golden hour around sunrise and sunset when light is warmest.
On a cloudy day, shadows are weaker. This can be good or bad depending on the situation. Strong shadows can make for striking photos, but the even lighting on cloudy days means less worrying about over or under exposing parts of your photo.
Overcast days can also set the stage for some unusual images. The surface of this pond appears white because it is reflecting a cloudy sky. Birds themselves may also look or behave differently in different weather, and it is valuable to document this.