Negligible normally means that something is so unimportant, that it isn't worth considering. In cryptography, a function of a parameter $n$ is negligible if converges to $0$ faster than $1/n^c$ for any constant $c>0$.
Negligible means that something is so unimportant, that it isn't worth considering. For example, if a flaw in a cryptographic algorithm is considered to be negligible, it is insignificant to both the algorithm as well as it's security.
In the complexity-based modern cryptography, a security scheme is provably secure if the probability of security failure (e.g., inverting a one-way function, distinguishing cryptographically strong pseudorandom bits from truly random bits) is negligible in terms of the cryptographic key length $n$. That is: the probability of success of the adversary (or their advantage in some experiment) is a negligible function of $n$.
A function $f:\mathbb R\to\mathbb R$ is negligible iff $\forall c>0$, $\exists N$ such that $\forall n>N$ it holds $|f(n)|<n^{-c}$.
