Different dogs will bark at different things (obviously), but a common theme with Jack Russells is that they often bark when they are bored, anxious, or excited.

The best first step is to keep track of the situations in which he barks (e.g., stimuli, time(s) of day, location) and what other types of behavior he displays in these situations. From those observations, try to deduce what he is feeling at the time. For example, (1) if he is wagging his tail, he is likely happy or excited; (2) if he is crouching down, he is likely scared or nervous; or (3) if he is laser-focused on his target with his hair sticking up, he is likely feeling threatened.

Boredom is the easiest to treat -- try tiring him out by taking him on longer morning walks, running him in the morning, or just having an extended morning play session. You could also try providing him with "entertainment" -- frozen peanut butter-filled KONGs generally do the trick for hours!

For anxiety-related behaviors, you can try to reduce his exposure to some triggers (e.g., do not let him in areas/on surfaces from which he often looks out the window and barks at things he sees outside). For separation anxiety, you want to go the other way, and repeatedly expose your dog to the trigger (i.e. you being away from him). The best way to go about this is to start by leaving him for short periods of time, and then giving him a treat when you return. Slowly lengthen the amount of time for which you leave him, but always give him a treat when you return.

I hope this was helpful! Best of luck :)