TITLE: What's so "schematic" about schemes?
QUESTION [11 upvotes]: Well, the title clearly follows the title of this question.
Why the objects so successfully defined by Grothendieck have been called "schemes"? In my opinion the original French word (schéma) doesn't help, by itself, to understand the motivations behind such a choice of nomenclature...

REPLY [10 votes]: In this context, the introduction of the word schéma is due to Claude Chevalley.
According to Dieudonné (The historical development of algebraic geometry, Amer. Math. Monthly, vol 1979, 1972, p. 827-866), nobody had ever given "an intrinsic definition of an affine variety'' until the 1950s, ie "independent of any imbedding".
For general varieties, Weil's definition used local charts, as in differential geometry and
Chevalley had asked himself what was invariant in Weil's definition. 
Cartier (Grothendieck et les motifs. Notes sur l’histoire et la
philosophie des mathématiques IV, 2000), himself quoted by Ralf Krömer (Tool and object: a history and philosophy of category theory, §4.1.1.1, footnote 319, page 164) explains that

La réponse, inspirée des travaux antérieurs de Zariski, était simple et élégante: le schéma de la variété algébrique est la collection des anneaux locaux des sous-variétés, à l'intérieur du corps des fonctions rationnelles. (Krömer's translation: The answer, inspired by previous work by Zariski, was simple
  and elegant: the scheme of the algebraic variety is the collection of local
  rings of the subvarieties inside the field of the rational functions.)

Soon after, Grothendieck's schémas pushed this idea even further.