"Awfully" is an adverb like "very", "really", "slightly", and so on. It can mean two different things:

1. When you're talking about something negative, "awfully ___" can mean "a little too ___":

   She's awfully close to the edge there. Tell her to come back over this way.

   You must be awfully tired. I'll go get the bed ready for you.

2. "Awfully ___" can also mean something between "quite ___" and "very ___":

   Oh wow. That was awfully nice of him to let you do that.

   I'm awfully proud of you, son.

The most common adjectives to use with "awfully" are:

• awfully good
• awfully nice
• awfully big
• awfully quiet
• awfully long