Many people have a number of signatures they like to use with various email correspondences and email addresses. You set these up in the "Signatures" section of Mail's preferences, but when you try to set a default signature to use, the "Choose Signature" menu is grayed out and set to "None".
In order to use this menu, you must first select one of your email accounts and then set the default signature for that account using this menu. There is no global setting for the default signature; rather, this is set on a per-account basis in Mail. This may not be apparent to some users, especially since Mail initially shows the "All Signatures" list with one highlighted. Additionally, while signatures are done on a per-account basis, they must first be associated with an account before you can choose one as the default. To do this, go to your "All Signatures" list and drag the ones you wish to use to their respective accounts. Then set each account's default signature.
Still not working? Delete signatures plist
Mail signatures are identified through the use of UUIDs (Universally Unique Identifiers) which are associated with your various email accounts through a property list called "SignaturesByAccount.plist". If there is something wrong with this plist file, deleting it may help Mail regain the ability to associate your signatures with their respective accounts again. This file is called "SignaturesByAccount.plist" and is located in the /username/Library/Mail/Signatures/ directory. Moving this file to the trash and relaunching Mail will clear your signature associations and allow you to set them up again.