Minecraft Server is used to run multiplayer Minecraft games on worlds of your (and others') own making.
Minecraft is a world-famous game by the indie developer Mojang. Initially released several years ago as of this writing, it has become so popular that it is a minor feature in Microsoft's latest operating system, Windows 10. Knowing that, it's undeniable that Minecraft has had a huge effect on the gaming world – right up to bringing tons of new people into the gaming fold.
In Minecraft, you play as a character made of huge 3D pixels ("voxels"), by default a man in a shirt and jeans named Steve, as you explore an enormous, randomly-generated world made out of square blocks of grass, dirt, and stone. Even the world's trees and structures are formed out of discrete 3D blocks, and it's those same blocks that players use to build homes, places, and even complex machines that serve various purposes.
Minecraft is simple to pick up and play, but with a lot of depth to master. For that reason, it's popular with all sorts of players, from the new to the old. and many players have their first experiences (or at least most of their experiences) with multiplayer games of Minecraft, where players share one of those huge worlds.
The Minecraft server hosts players in these shared worlds, often up to 32 players at a time. It is not the game itself, although on the other hand, this means that you generally do not need to own the game (or have it on a given computer) to run a Minecraft server. In addition to its obvious use of running the game itself, a Minecraft server admin can chat directly from the server with players on the world, or change various world settings (such as the current time of day).
Many Minecraft servers are "modded" to introduce new gameplay modes beyond Minecraft's normal "Survival", "Creative", "Adventure", etc. modes, or to add features (such as new animals or areas) to those existing game modes. The Minecraft server itself does not provide those mods, but can be extended with those mods in a process that ranges from easy to difficult depending on the individual mod.
The server itself is easy to use, so for someone who wants to try hosting a Minecraft server, it is very easy to get started by not using mods. Otherwise, it is easy to learn the program and, later, how to install mods.