"With a purposeful grimace and a terrible sound
He pulls the spitting high-tension wires down
Helpless people on subway trains
Scream, bug-eyed, as he looks in on them
He picks up a bus and he throws it back down
As he wades through the buildings toward the center of town
Oh, no, they say he's got to go
Go, go, Godzilla (yeah)
Oh, no, there goes Tokyo
Go, go, Godzilla (yeah)"
- – Blue Oyster Cult, Godzilla
CoDzilla is a 3e Dungeons & Dragons term, a portmanteau of "Cleric or Druid" and "Godzilla", describing a very powerful Cleric or Druid build. It came about because these classes have the potential to become game-breakingly overpowered when built properly. So great is this problem that playing a straight cleric or druid is often referred to as "Playing D&D on easy mode." Some other builds with similar levels of power include the Batman Wizard/Erudite, the Inspector Gadget Artificer and the Librarian Archivist. Some of the only builds even more ripe for abuse (i.e. ranked at Tier 0) include the Beholder Mage (knows every spell, gets a large number of spells per day, can cast 10 spells per round spontaneously and has a lot of nifty abilities? Why not?), Illithid Savant ("anything you can do, I can do better"), Thrallherd (which can use this build as a FUCKING CLASS FEATURE) and Pun-Pun.
In addition to wielding considerable magical power that rivals that of the other reality-twisting classes - Wizards and Sorcerers, the other big reality-twister being maybe the Erudite - CoDzilla also receives better combat skills and abilities, such as the ability to wear heavy armor (for Clerics), better base attack bonus progression and, in the case of Druids, the combination of the wild shape class feature and the Natural Spell feat (which allows the druid to cast spells even while shapeshifted, when they already have considerable ability score buffs.) By proper application of its powers (and a halfway-decent selection of feats and domains,) CoDzilla is able to dish out massive melee damage and take punishment to a degree that greatly surpasses regular fighter or barbarian-types and equals (maybe even surpasses) ubercharger, shock trooper, hulking hurler and other full-BAB builds. Meanwhile, one still enjoys additional advantages such as full casting (which as anyone with any experience with the game knows is immensely powerful, especially the kinds of full casting that don't have a limited number of known spells), throwing the game out of balance.
For example, with the strength domain a cleric can boost his Strength score to absurd levels for one round (we're talking about a bonus equal to his level.) Combine this with Righteous Might, Divine Power, Divine Favour, charging, using a two-handed weapon (preferably a +5 impact Minotaur greathammer,) pounce, a +5 inherent bonus to Strength, and expending as much to power attack as he can get away with; the damage done with a full attack would be enough to kill 99% of the monsters in the monster manual in a single round and put a serious hurting on anything that can survive. This, of course, is far from the most optimized CoDzilla build.
With gestalts, one can create the (un?)holy/axiomatic/anarchic/neutral abomination that is the CaDzilla (cleric and druid zilla.) What we have here is essentially combining all the buffs, debuffs, healing spells, domains and access to Divine Metamagic of a cleric with the wild shaping, other buffs/debuffs and other nifty spells that druids are so fond of. Lets also not forget the Animal companion, who nicely fills the meatshield role of a melee martial character, as well as spontaneous Summon Nature's Allies and access to both classes' impressive spell lists. Use Greater Magic Fang to replace magic weapons, or perhaps a mouthpick magic minotaur greathammer, and at this point you're just showing off. The party's non-fullcaster members will only be able to look upon the destruction you can wreak and weep as you completely and utterly outperform them.
4e has largely fixed such issues by leveling the playing field for all classes, primarily by greatly reducing the abilities of spellcasters to put them in line with nonspellcasters (read "made everyone a bard"). Minmaxing touhoufags have nevertheless proven that 4e still has its share of broken builds, but they are generally not nearly as all-encompassingly powerful as the dreaded CoDzilla.
5e has dealt with this by preventing any caster from having more than one active buff spell via the Concentration mechanic. Essentially, if a spell has the Concentration tag, then that means that your caster has to mentally focus on keeping the spell up for the listed duration, if you get attacked then you have to roll a special Constitution check to see if the attack breaks your concentration, in which case the spell turns off. Every single caster is only able to have one concentration spell going at once. This prevents clerics from buffing themselves to godmode levels because they can only use one spell as a buff, and all the buff does is give advantage, which doesn't stack, so clerics can no longer become Rage McHuegSmash in one round (at least at this point). They've also removed the Druid's animal buddy, seeing as he didn't especially need it.