I know that $$A\Rightarrow B$$ means that $A$ is a necessary condition for $B$ and $B$ is a sufficient condition for $A$.
Also, $$A\Leftrightarrow B$$ means that $A$ is necessary and sufficient condition for $B$ and vice versa.
Is there any other relation that are neither necessary nor sufficient conditions? (Maybe my question depends on the context? or it is very board?)
Actually, if $A\implies B$, then $A$ is a sufficient condition for $B$ and $B$ is a necessary condition for $A$. It makes sense that way since $A\implies B$ means that if you have $A$, then you get $B$ for free, meaning that having $A$ is enough (is sufficient) for having $B$. On the other hand, if $A\implies B$, then if you do not have $B$, you also do not have $A$ since $\neg B\implies \neg A$. This means that if you want $A$, you at least need $B$, making $B$ a necessary condition.
As for other conditions, well, if they are neither necesary nor sufficient, you can hardly call them conditions, don't you think?