Originating in Dave Arneson's First Fantasy Campaign, Alignment is a concept used by role-playing games used to grade the personality of a character. Several models for this system exist: the most famous is the 3x3 grid used by Dungeons and Dragons from 1st edition AD&D until D&D 3.5.
Alignment is a hotly debated topic, mainly because it is perceived as an oversimplification of the human nature that has been explored by all kinds of writers, scholars, philosophers, theologists and sociologists. Some players feel limited by this system and downplay its importance. Other systems do not contain such a system at all, giving the players more freedom to do what they want with their characters.
Mechanically alignments can have some degree of influence on the game: certain spells or items only affect certain alignments or cannot be used by them, clerics need to have a certain alignment in order to gain spells from their god, and some classes only get their features if they are of a certain alignment.
Please note that questions about "what alignment is person/act/society X" are off topic due to subjectivity, see What Kinds Of Alignment Questions Are On Topic? for more.