The genre of mecha, both as a medium and a form of animation, were introduced to the world very soon after World War 2 with Japan's Astro Boy in 1963. Though there were already signs and hints of the interest towards sci-fi fantasy robots in media beforehand, Astro Boy is the series that truly embodied and pioneered what the medium is today. Shows like Mazinger Z (1972) and Gigantor (1963) revolutionized the themes of Astro Boy, and truly introduced the idea of giant machines with super powers. It was because of shows like these that Super Robot shows were so incredibly common during this time, and also laid the groundwork of what was considered the norm of the mecha genre as a whole.
As the genre developed, the main hard hitting series that evolved the themes and ideas in 1979 was the Gundam franchise, debatably the most iconic and revolutionary Japanese anime of all time. It was with Gundam that the mecha genre split into 2 primary groups, the ones that stuck with the Super Robot themes but now realistic, darker stories with much more series themes; primarily war and human ignorance. It has gotten to a point where people unaware of any mecha shows tend to refer to any robot with 2 glowing eyes as a Gundam.
However, in the West that is fairly different as another series takes the cake for iconicism; Transformers. In 1986, the first Western animation featuring giant robots took stage and essentially dominated the public conscious in the United States and revolutionizing the genre once again, truly making the giant robots actual characters rather than glorified tanks or tools for humans. It is these 2 series that absolutely own what makes up the mainstream view of mecha shows.
Watch what many people regard as the best mech fight to date