$\newcommand{\P}{\mathbb{P}}$ The general intuition for forcing (at least for me) is that forcing with $\P$ doesn't dramatically affect objects of size $> |\P|$. Of course new large things appear, but these are usually "echoes" of something that happened lower down.
Recall that a poset $\P$ is $\leq\kappa$-closed if any descending chain in $\P$ of length $\leq\kappa$ has a lower bound. A poset $\P$ is $\leq\kappa$-distributive if forcing with $\P$ doesn't add new $\leq\kappa$-sequences of ground model sets. It is easy to see that any $\leq\kappa$-closed poset is $\leq\kappa$-distributive; however, the converse doesn't hold.
There are two closely related questions I want to ask here.
Firstly, suppose we have a forcing poset $\P$ which is $\leq |\P|$-closed (or $\leq |\P|$-distributive). Does this imply that $\P$ is trivial for forcing? If not, is there a bound $\kappa=\kappa(\P)$ such that any $\P$ which is $\leq \kappa(\P)$-closed (or $\leq \kappa(\P)$-distributive) is trivial for forcing?
And secondly, what if, in the above, we replace $|\P|$ with whatever the saturation of $\P$ might be. That is, if $\P$ has $\kappa$-c.c. and is $\leq\kappa$-closed (or distributive), is it trivial for forcing?