A (one-dimensional) formal group over $\mathbb{C}$ is a formal power series $F(x,y)\in\mathbb{C}[[x,y]]$ such that $$ F(x,y)=x+y + \text{terms of higher order} $$ $$ F(x,F(y,z))=F(F(x,y),z)) $$
Simplest example is $F(x,y)=x+y$. How did mathematicians come to this concept, what's the motivating background?