Tanks are
armored ground vehicles that travel on a
tracklaying chassis (also known by its most visible characteristic,
treads), and mount
weapons designed to
engage other vehicles of their own class (at a minimum) as well as be as
lethal as all hell to anything on the battlefield smaller or less protected than themselves. Tanks do come in various sizes, from
light tank all the way up to the behemoths known as
Main Battle Tanks.
Although fearsome in capability, tanks are not without several glaring and well-known vulnerabilities. First of all, they are extremely large, heavy and in most cases relatively slow-moving. This means that, barring other factors, hitting a tank with an aimed weapon once you've gotten a good look at it isn't a large problem. Therefore, designers and operators of the things have had to come up with various means to ensure that you don't get that good look, or that even if you do hit it, it doesn't care.
Second of all, because they're large and heavy, tanks are limited in where they can travel. A modern MBT can weigh as much as 75 tons and measure in at 8 meters by 5 meters! Running one of these through a cramped cityscape isn't possible unless you're trying to knock the city down as you go. This sometimes is the case. See Grozny for a recent example. However, in a more frequent problem area, tanks are limited to strong bridges and large transport vehicles, meaning bodies of water such as large rivers or lakes can cause real trouble for them. They are extremely difficult (although not impossible) to move by air.
Third, modern tanks are extremely complex machines, are require an enormous amount of routine (and, unfortunately, sometimes not-so-routine) maintenance in order to remain operational. They cannot typically be used to travel long distances; in between actual engagements (and sometimes during protracted ones) tanks must be carted about on large trucks or railway cars. At any given moment, a significant number of these large expensive and crucial assets may be out of service. They also, therefore, require a huge logistical tail to keep running, with a steady flow of fuels, lubricants, ammunition, spare parts, etc.
Fourth, tanks suffer from their very success. By their nature and due to their deadly capabilities, tanks are regarded as primary targets on any battlefield on which they appear. This results in an amusing dichotomy between tank crew and infantry - tankers profess to not understand why you'd want to be on a battlefield without several inches of high-grade armor around you, and infantry profess to not understand why on earth you'd want to spend all your time inside a high-visibility target, methods of whose destruction have spawned entire industries and technologies.
At the strong suggestion of the Management, this writeup has been split off. For a more (mind-numbingly) complete discussion on the modern tank, see the remainder of this exposition at Tanks: A Brief History and Hunting Guide!