The general idea is that when something is made up of many, many little things, it's difficult (if not logically impossible) to say that just one of those little things is what makes the big thing itself or, in another context, if very many minor actions cause something, then each of the individual causes is too minor to bother with calling it the cause of the major effect.
For example, if you have a few grains of sand, then it's not a heap, but if you have millions of grains of sand, it's definitely a heap. Say I take a heap of sand and start removing one grain at a time, at what point is the heap no longer a heap?
In the context of climate change, Garvey points out that what seems to absolve us individually from responsibility is that none of our individual actions is really contributing very much at all to the climate problem. In fact, this reason is sometimes given as a reason for inaction because if just one person stops adding to cumulative greenhouse gas emissions, that individual restraint won't do much of anything to curb the problem. However, since the heap is made up of individuals, the only way to face up to the problem is to somehow address the collective.
Here's a somewhat weird comic about the sorites paradox. Or maybe it's really about something else...
Source: Dinosaur Comics