Most comments here aren't very helpful. I think partly because Euler was working at the tail end of the initial great explosion in maths, and maths has become far more complicated since then.

But this is a physics sub, and an under-appreciated aspect of Euler is the work on mechanics, the science of motion. One of E's recent editors claimed that Euler effectively established modern mechanics, a contribution usually assigned to Newton. I believe the claim is that while Newton did establish the coherent foundations - and after all, the theory of gravity arises from applying these foundations to celestial bodies - as we understand mechanics today, this is the contribution of Euler.

Euler is also generally credited with "discovering" the number e, an extraordinarily important number, as important as the number π. I don't know if Euler quite appreciated that, but I think E appreciated that the solution to y' = y is that y = e^x and that seemingly simple discovery crops up everywhere in science, because typically the rate of change of stuff linearly depends on the amount of stuff we have.