Tanking generally refers to strategies that defend a ship against hostile fire. Most commonly it refers to the ability to maintain shields or armor, but it can refer to methods that prevent damage from hitting the ship in the first place.
Tanking can also refer to the tactic where one ship of a fleet draws the fire from the opposition while other members of the fleet act take advantage of this, by repairing the 'tank' or by carrying significantly greater offensive ability on the expectation of not being attacked.
Forms of tanking
Prior to the nano age and as of the last patch, which included the infamous 'speed nerf' the most widely encountered forms of tanking are shield or armor tanking, which can be broken down into three sub categories: Active shield or armor tanking, Passive shield tanking or buffer armor or shield tanking. Each one performs differently for different jobs.
Active tanking is the most common, and involves using modules that quickly repair your ships damage, ideally more than the ship is taking (blocking out all damage while maintaining a balanced cap is referred to as 'perma tanking' and means that an opponent is literally incapable of breaking your ship) although these modules require a large portion of your ships capacitor to run, which means you need to balance your cap as well. Striking a balance between using up all of your cap and blocking out all the damage your taking is tricky but is the most versatile and dependable form of tanking. Both armor and shields can be active tanked.
Passive (shield) tanking
Passive tanking is only available to shield tankers and involves making sure you shields recharge themselves quickly. As the name implies, a true, full passive tank should require no modules that need to be 'turned on' unlike its cousin the active tank, therefore capacitor is not needed to run a passive tank (tho some people use a semi passive tank that uses invulnerability fields). The drawback to passive tanking is its hard to fit any useful modules to your ship for other tasks, which makes passive tanks somewhat of an enigma. Also although some players can pull it off, most passive tanks only work properly on battlecruiser class ships, with cruisers having too few slots to warrant anything other than an active or buffer tank, and battleships being to big to be able to effectively recharge the shields. Passive tanks differ from active tanks in that they don't really block out the damage received, but slow down the rate of shield decline instead. The advantage of this over active tanking is that if an active tank receives more damage it can handle it will fold very quickly, where as a passive tank will give you plenty of warning that something has gone wrong and you need to flee. Passive tanking is also 'in fashion' in eve and is used regularly to handle tough missions.
Buffer tanking is based around the principle of having as many hit points and high resists as possible. The pilot may fit active or passive resistance modules, which complement the 'buffer' modules. These are fittings that simply add more hit points to your ship. A good buffer tank will usually be able to fit more combat utility mods including, but not limited to heavy energy destabilizers, heavy turrets, sensor boosters or tackle. As buffer tanking takes the least slots to make work and uses less fitting than passive or active tanks it is used mainly for PvP and not PvE. Even though the drawbacks to buffer tanking are numerous, you cant repair yourself, extra armor or shield mods slow you down and they need high resistances to work, in the right hands a good buffer tank is a hard thing to fight against.
Up until the recent speed nerf, speed tanking was a very popular form of tanking, and is still viable even now ships are slower in Eve. Speed tanking means you can outrun missiles or drones, and move too fast for guns to track you. Speed tanking would normally lead to intense dogfights where you would have to attempt to outrun your opponent in order to catch them, or escape.
Speed tanking also leads to the much underrated 'range tanking' whereby you fit your own ship to engage at very long range, possibly up to 150 or even 200 kilometers from your enemy, and to move fast to be able to maintain that range. As most people don't fit range mods range tanking is having a renaissance in light of the speed nerf amongst savvy pvp'ers. Speed tanking is still possible in smaller ships, frigates, tech 2 frigates and tech 2 cruisers, it is just less reliable now than it was before.
Another alternative form of tanking is hull tanking. Eve does support hull tanking as a viable option as there are modules available to repair and resist damage to the hull of you ship, however its a whacky, weird form of tanking that only the elite bother to try. As such a much quoted phrase 'real men hull tank' has sprung up in the world of Eve, meaning that to effectively tank damage on your hull requires some specialized skills and balls of steel.
Certain forms of attack are seen as more of a defense than an offense, to the point that a heavy ECM boat is sometimes referred to as ECM tanking as it relies on stopping the opponent from locking your ship in the first place. Another method is using modules to drain the opponent's capacitor, greatly limiting his ability to make use of weapons (that require power), as well as denying the use of active defenses.