what does the word precipitate mean?

In this instance, it means to cause, “…candidate for public office cause social change?”

Another way to put it would be to “bring about” social change.

I think the word “precipitate” as a little finer meaning than simply to “cause” or to “bring about”. For example, the technical name for the natural occurrence of “rain” is referred to as “precipitation.” Although all rain requires clouds, not all clouds bring rain. To make rain or precipitation requires a number of elements and conditions to be present. And, until all those elements and conditions are present, rain does not occur.

In this broader sense, your question about “thoughtfully casting your vote” takes on a little different meaning in considering how it might “precipitate social change.” I think the question asks you to consider all of the factors required to cause or bring about social change and how a thoughtful vote for a winning candidate is a critical element that finally makes the change possible. Just like the fact not every cloud brings rain. So, it is not all votes bring social change. I think the questions asks what is different about a particular vote that actually does create social change.

1 : having the power of or actually driving or impelling 2 a : arising from an impulse b : prone to act on impulse 3 : acting momentarily

in that sentence it means cause