An Acronym for InterNet Assigned Numbers Authority.
By consesus, they allocate various things, such as port names/numbers and many networking protocols - see http://www.iana.org/assignments/.
Probably the most well-known task is allocating IPv4 address space to the various international registries (such as ARIN, RIPE, APNIC, LACNIC, etc). This is done by delegating ClassA networks to those agencies which then assign them to organisations in those areas. See http://www.iana.org/assignments/ipv4-address-space/.