I'll assume that you have a dictionary and that you have already looked up the "standard" meaning of the word and that you are trying to figure out the everyday usage one hears on TV or on the street.
It's mostly a word used by people under 30 to describe a general feeling of great satisfaction or wonder at what they have just heard or experienced.
How was the concert?
It was awesome!
Jim - "I've been trying to get her telephone number for weeks and she finally gave it to me yesterday."
Joe - "Awesome, now you can ask her out."
Look at those waves!
PS: many say its origins were in the San Fernando valley suburbs of the city of Los Angeles, California.
Student or Learner