They do, indeed!
The clock has a barometric air pressure sensor at its core that continually measures the atmospheric air pressure throughout the day.
Even inside a relatively air-tight home the air pressure changes are sufficient for your clock to forecast from, as you will see.
By monitoring the air pressure, the clock can tell whether it is rising or falling in relative terms over time – an important aspect of weather forecasting.
Very simply, if the clock notices the air pressure is rising then it will forecast sunnier weather. Conversely, if air pressure falls then the clock will forecast rain. The faster the rate of change, the more extreme the swing in either direction.
Here's a video explanation by Bramwell Brown's Co-Founder, Rob: