What is the meaning of Sheaf?

A quantity of the stalks and ears of wheat, rye, or other grain, bound together; a bundle of grain or straw.

Any collection of things bound together.

A bundle of arrows sufficient to fill a quiver, or the allowance of each archer.

A quantity of arrows, usually twenty-four.

A sheave.

An abstract construct in topology that associates data to the open sets of a topological space (i.e. a presheaf) in such a way so as to make the local and global data compatible, generalizing the situation of functions, fiber bundles, manifold structure, etc. on a topological space. Formally, a presheaf ${\displaystyle {\mathcal {F}}}$ whose sections are, in a technical sense, uniquely determined by their restrictions onto smaller sets: that is, given an open cover ${\displaystyle \{U_{i}\}}$ of ${\displaystyle U}$:

1. If two sections over ${\displaystyle U}$ agree under restriction to every ${\displaystyle U_{i}}$, then the sections are the same.
2. Given a family of sections ${\displaystyle s_{i}\in {\mathcal {F}}(U_{i})}$ such that all pairs ${\displaystyle (s_{i},s_{j})}$ agree under restriction to ${\displaystyle U_{i}\cap U_{j}}$, there is a (unique) section ${\displaystyle s}$ over ${\displaystyle U}$ whose restriction to ${\displaystyle U_{i}}$ is ${\displaystyle s_{i}}$.

If two sections over ${\displaystyle U}$ agree under restriction to every ${\displaystyle U_{i}}$, then the sections are the same.

Given a family of sections ${\displaystyle s_{i}\in {\mathcal {F}}(U_{i})}$ such that all pairs ${\displaystyle (s_{i},s_{j})}$ agree under restriction to ${\displaystyle U_{i}\cap U_{j}}$, there is a (unique) section ${\displaystyle s}$ over ${\displaystyle U}$ whose restriction to ${\displaystyle U_{i}}$ is ${\displaystyle s_{i}}$.

To gather and bind into a sheaf; to make into sheaves

To collect and bind cut grain, or the like; to make sheaves.

Source: wiktionary.org