Intuitive meaning of Exact Sequence I'm currently learning about exact sequences in grad sch Algebra I course, but I really can't get the intuitive picture of the concept and why it is important at all.
Can anyone explain them for me? Thanks in advance.

Here is a topological interpretation:
Let $X$ be a space and $Y$ its subspace. If a boundary (in $Y$) of an $n$-dimensional relative cycle $c$ of $X\setminus Y$  is a boundary of something in $Y$ then one can build a proper $n$-dimensional cycle of $X$ from $c$, gluing this "something" to $c$.
