In the Mentions Report you can check out how many times you've been mentioned on a particular day.
You'll be able to notice peaks or drops and act accordingly. Maybe you'll find that taking part of a Twitter Live Chat does wonders for your Mentions.
You'll also be able to compare Mentions to another metric, e.g. Followers. To see if there's a positive relationship.
And of course you can export this data and change the date range.