There are many different behaviours your bearded dragon may exhibit, most of which make them so interesting to watch, some of these things include:
Climbing - Bearded dragons are semi-arboreal so love to climb higher than the ground, unless out of the vivarium my bearded spends 75% of his time climbing, even so he will try climbing the net curtains.
Brumation - This is the process whereby over the cooler/darker winter months, your dragon will 'hibernate' so to speak, and during this period they will sleep much of the time. They tend to be generally rather inactive and eat far less than normal. However, a reduced temperature (heat) and UVB light should continue to be provided along with food as normal. You should try and avoid allowing your bearded dragon to brumate until they are older and have padded out slightly (over 1 year).
But – if your bearded dragon has its mouth wide open for prolonged periods of time, it may be overheating. Check the temperatures in the vivarium and confirm they are correct. You can also drop a little water on its nose if it is dehydrated.
Twitching - If your bearded dragon is twitching, it could mean that it has a lack of calcium or UVB. Make sure you are dusting your live food with calcium powder and even sprinkling it on its salad (if it still eats it like this). Seek your reptile vet's advice if this continues.