I'm gonna guess that you are fairly new to the game and weren't here for Season 2 or the beginning of Season 3.
Basically, the game is VERY different depending on whether tanks are strong or not.
Season 2 had Super Tanks that literally just would not die unless the AD Carry was allowed to just go ham on them. Killing the AD Carry meant that the enemy team would not be able to kill your tank...at all...as in you won the fight as soon as the enemy ADC died. Strong tanks could put out some pretty impressive damage with Sunfire/skills/basic attacks while having tons of CC and with items like Force of Nature, the dreaded Fratmogs (Frozen Mallet, old Warmogs, and Atma's Impaler), and Triforce for damage tanks, any champ that relied on cooldowns for damage would die long before they could get enough ability rotations to kill a tank. In this meta, Mages were stuck mid and Assassins and AD Casters were bad most of the time since they weren't good at protecting the carry and if they failed to kill the enemy carry then they just lost their team the game.
Season 3 had the ridiculousness that was Runic Bulwark. It provided so many free stats in an aura that the support and the jungler and sometimes the top laner were all obligated to get one just to match the enemy team getting 2-3 of them. This meant that tanky top-laners and junglers were priority picks and that all members of the team had a surprising amount of tank stats. Fights could really drag out and when team fights drag out because targets are too tanky to be insta-deleted the whole meta changes for that. Mages had problems because EVERYONE had way more MR than normal, and sometimes even got replaced by bruisers mid. Assassins and AD Casters were really situational...they often failed to gib the enemy ADC since team comps were very tanky all around and favored having lots of people with tanky builds and CC hovering around the ADC to overlap the auras.
Once tank items were nerfed or removed, and some tanks directly nerfed, it just became more practical to do AoE, siege, poke, or pick comps and people got used to seeing only one tanky member on a team and comps that focused on combo'ing damage so fights ended very quickly and favored champs that could end fights fast or clean up well after a good engage. Obviously Assassins and AD Casters have dominated for a bit due to the high number of squishy targets.
Which brings us to now.
Cinderhulk made tanks much tankier than they had been before, thanks to huge bonus HP increase and the effect of Armor/MR on tanks making the effective HP increase much, much higher. Some tanks have also been buffed and started seeing more play. Between tanky champs in top lane, the high effectiveness of tanky supports like Leona to counter Thresh, and new tanky junglers being used...there just aren't as many viable targets for Assassins. Combined with the mana-regen nerfs which severely hurt most mages, itemization changes like the removal of DFG, and continued nerfs to Assassins, and we get the current situation. Assassins and AD Casters are back to being situational, Mages have been feeling less powerful lately, and several tanky Fighters were taking Cinderhulk top so they could be much tankier than they were previously with comparable damage. It feels like teams are tankier overall and fights are lasting longer so strategies and champ picks change.
TL;DR - A "Tank Meta" occurs any time that itemization changes and nerfs to Mages and/or Assassins favors tanky champs, especially if running tanky champs both top lane and jungle (sometimes even Support) is not only possible, but actually a strong strategy. It will stop being a "Tank Meta" when tanks are less valuable and running more squishy champs in a team comp becomes practical again.