Statics are just a group of players who agree to tackle (mostly endgame) content at the same pace.
In FFXIV statics are formed mainly to tackle the harder content in the game, Savage and Ultimate Raids. They require a substantial amount of coordination and memorisation. If you don't have a static, you can join pick up groups (Pugs) in game using the Party Finder and try stuff with randoms.
Can add me to the CWLS - Hanningfield Ward (Odin server). Usually just on Lv80 DRG, but have been wanting to level more range and maybe Heal/Tank also.