what are the most critical functions of the global traffic manager?

I would say there are three main functions within the GTM product:

gtmd - This is your wide IP configuration, along with the supporting pools/servers and any iRules. Any FQDNs requiring load balancing should be configured here.

ZoneRunner - essentially ISC BIND. Underlying process is named, generally used if you don't need any special load balancing capabilities and you want to hand out static records.

DNSSEC - you define zones and keys to apply to those zones to secure them with DNSSEC.