Every gardener is something of a weather watcher, since the well-being of our plants hinges on temperature and precipitation, and our gardens live under the whims of the wind and the clouds. While we can't do anything about the weather, it's nice to know what to expect so we can take action to protect or help our plants if need be. Aside from these practical points, I think a lot of us are just plain interested in the weather for the same reason we're interested in gardening—an appreciation of the nature.
You might have some basic weather-watching tools of your own, and I'm sure you have a trusted source for your local weather report, perhaps a favorite TV meteorologist who never seems to get it wrong. A great online resource is the website of the National Weather Service, www.weather.gov. One thing I like to do is click on my location on the map on the homepage. That gives me a "Quick Glimpse" at the weather in my area . . . and even better I have the option to click for local watches, warnings & advisories—such as a frost warning.
I encourage you to explore weather.gov!