The DNS works on a question-answer model. If a client needs information from the DNS it sends a question to a DNS server and the server returns an answer. Until recently it was only possible for a server to examine a question and determine whether or not to answer it based on the IP address the question originated from. This is not ideal. Authentication using source IP address alone is considered insecure. Transaction Signatures, or TSIG for short, add cryptographic signatures as a method of authenticating a DNS conversation. It uses a shared secret to establish trust between the communicating parties.
TSIG is used to ensure that DNS information purporting to be from a certain server is actually from that server. I have mostly put it to use to authenticate zone transfers between master and slave nameservers. I want to be sure that my slave nameserver is never fooled into accepting a copy of my zone from an imposter who spoofs my master nameserver's IP address.