In our CEO’s book, Managing Mission Critical Domains & DNS, he called SRV records “The Swiss Army Knife for DNS”. They can be thought of as a kind of all-purpose “MX-ish” record that can convey additional information such as weighted distributions and alternate ports.
They are used in conjunction with applications that specifically query for and expect to find SRV record responses.
Some examples include:
LDAP services
Active Directory
Kerberos
XMPP/Jabber
Session Initiation Protocol (SIP)
Puppet
Minecraft
SMTP submission
DANE
CalDAV
(Alas, no major browsers seem to support SRV recs, otherwise you could easily do weighted load-balancing and alternate port-mapping right from here.)