“It's awfully cold for March.”

You're making small talk with a friend about the weather. It's March, when the weather usually starts to get warm, but today it's snowing. You say:

It's awfully cold for March.

awfully (something)

"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.

In the example above, "awfully cold" means it's very cold or quite cold. 

(adjective) for (something)

When you say that it's "cold for March", it means that the weather is colder than March days usually are.

You can say that something is "___ for ___" whenever you want to compare it to other items in a similar group. For example:

It's a good value for the price.

You speak Korean well for an American.

The atmosphere of St. Laurent's is surprisingly down-to-earth for such a traditional French restaurant.