Question

Pointers to questions on mathoverflow which contain directly relevant material, or describe how algebraic geometry diffuses through the soil nourrishing scientists' thinking:

http://mathoverflow.net/questions/62866/recent-applications-of-mathematics/62876#62876

http://mathoverflow.net/questions/84003/are-there-some-original-papers-or-books-related-to-applications-of-algebraic-topo

http://mathoverflow.net/questions/36471/facts-from-algebraic-geometry-that-are-useful-to-non-algebraic-geometers

http://mathoverflow.net/questions/29271/algebraic-geometry-used-externally-in-problems-without-obvious-algebraic-struc

http://mathoverflow.net/questions/77195/how-has-modern-algebraic-geometry-affected-other-areas-of-math

http://mathoverflow.net/questions/62677/applications-of-commutative-algebra

http://mathoverflow.net/questions/36471/facts-from-algebraic-geometry-that-are-useful-to-non-algebraic-geometers

http://mathoverflow.net/questions/2556/real-world-applications-of-mathematics-by-arxiv-subject-area

In general studying the works of Bernd Sturmfels (and his many outstanding collaborators) will be of great interest if you are looking for applications. But much of algebraic geometry illuminates directly only other areas of mathematics, the "algebraic" structures it treats arise from layers of abstractions and are usually not visible in the real world model without some work. (For instance surfaces do not come with an algebraic structure in nature but all of them admit many, parametrized by moduli spaces, which may be useful when studying dynamics on them, and dynamics of related systems appearing in nature, c.f. here.)