Of the six stats, Strength represents both physical might and the physical prowess to apply it properly. It is used for most hand-to-hand attack and damage rolls, most combat maneuvers like grappling or knocking enemies prone, and for breaking physical objects, as well as for less-violent tasks like determining a character's carrying capacity or a variety of physical Skills, like Climbing, Swimming, and overall Athletics. It also offers the muscle necessary to wear heavy armor without penalties and melee weapons with the thrown keyword can be used to make ranged attacks with Strength instead of Dexterity.
Strength is intuitive and easy to understand, but it does suffer often in comparison to its cousin Dexterity. While it is the primary skill for melee combat, it is also fairly easy to use as a dump stat for characters who wish to avoid melee combat, since its major penalties for dumping (such as reduced carrying capacity and ability to swim/climb) are easy enough to pass off, via buying a literal or figurative packmule or casting spells to let one fly. Still, it's an overall useful and rewarding stat to specialize in, and there are at least a few things that it can do and Dexterity can not even in 5e.
Strength is, obviously, one of the three "physical" stats. The classes most associated with it are the traditional heavily-armored fighter and paladin, as well as the raging barbarian, though any class that wishes to do damage in melee combat in editions where Dexterity can't be easily applied to melee damage should at least invest a bit into it. Spellcasters may also need it to make "touch" attacks with their spells, though these are often easier than normal melee attacks or use a different ability score.