These settings allow you to connect a Twitter account with the collection via a Twitter Application. Anytime a new webcomic is published in the collection a status update will be made to the account you authorize in the format you specify using your Twitter Application.
Visit Twitter Developers to create a new Twitter Application. You'll need to sign in with a Twitter account (any will do; this does not have to be the account you plan on tweeting new webcomics to) and then fill in the required information. The optional Callback URL setting of your Twitter Application must be set to your site URL (you can find the correct URL in the Help tab on the collection settings administrative page).
Once created, go to the Settings tab for your Twitter Application and ensure that Read and Write is selected for Application Type. Then return to the Details tab and copy the Consumer Key and Consumer Secret values into their respective fields on the collection settings administrative page. If the keys are entered correctly a Sign in with Twitter option will appear in the Authorized Account area on the collection settings administrative page.
Clicking the Sign in with Twitter link will direct you to Twitter's site, where you'll need to authorize your Twitter Application to tweet to your Twitter account. Once authorized you can return to the collection settings administrative page. Webcomic will display the Twitter username that has been linked to the collection in the Authorized Account section. You can revoke this authorization at anytime from your Twitter settings, or simply remove the Consumer Key and Consumer Secret settings, which will prevent Webcomic from connecting to your Twitter Application.
Once you're all linked up you can customize the Tweet Format used when Webcomic posts to your Twitter account. The Tweet Format accepts a number of tags, but don't go crazy; remember the 140 character limit:
When Upload Media is selected Webcomic will send the first full-size media attachment along with the tweet it publishes. The media attachment will be uploaded to pic.twitter.com and displayed with the tweet.