Does updating the post date help? Maybe/probably a tad, but it may not be in the way that you're thinking.
There is a lot of confusion on this topic (and understandably so).
Why? Because there are 2 "conflicting" things going on here. First Google generally prefers older content and older sites. (These sites and articles tend to have more credibility and authority and part of that may be due to backlinks).
Second, Google prefers "freshness." (Note: fresh content and freshness are not necessarily the same).
So really, the ideal is usually a combo - older content that you update with fresh content (e.g. update every 6 months or so).
It is doubtful that just changing the date will make a difference for Google. They are pretty smart and they know the original publish date. They also use the last modified date. And, they compare the current version vs previous version. And, if it's virtually the same, they pretty much ignore it (more on that in a bit).
Now, while just changing the date (and nothing else) probably will not have a direct impact on your ranking, it may have an impact on your click-through rate on both the search engines and Pinterest. This in turn may help you move up the rankings a bit, as click-through rates can impact your results.
This will of course vary based on the topic and how relevant the date is to the topic. If I'm writing about the latest home decor trends, it will probably matter more; if I'm writing about different species of hardwood, it probably matters less (as those stay pretty constant).
Google ranks more on content changed rather than superficial changes such as the date. And, in general when it comes to SEO, if something sounds too good to be true or too easy, it usually is. If I could just boost my post by updating the dates, I'd write a program of something to update the date every day...it doesn't work.
Anyway, here's my advice.
If you have made significant changes to the article, update the date on the post. It only takes a minute. If you haven't made significant improvements, don't. Don't be like the boy who cried wolf.
Now of course I oversimplified a bit above, so I will go into more depth below, as well as show you how to update the dates.
Freshness queries vs more evergreen queries
First, for the record, newer content doesn't get a boost. If anything older content and content on more established sites have an inherent advantage.
But, it does vary based on the query, and of course years ago, Google filed a patent on a freshness factor. But bear in mind it's a factor (and there 200+). Importantly, it will vary by the category and query.
According to a former Google Fellow (Amit Singhal), different category searches have different freshness needs. So they measure the freshness scores for each page but the importance of the factor will vary based on the type of search.
For example, freshness would matter more for:
Recent events (this might include things like current events, unfolding stories, google algo changes, etc.)
But it would be less important for topics that don't change much such as:
Historical events (e.g. WWII, Fred Astaire's life, etc.)
And, many other topics lie between these 2 extremes
How to change the date on your posts
If you have Wordpress, this is easy. Just go to edit your post and on the upper right, find the Publish section in the right sidebar (this is where it is on most themes).
Find the publish date and click the Edit button next to it (see the blue arrow). Update the date, then click okay and then save.
2 very important notes below.
1. If you are changing the date to be today, be sure to check the time. If the time hasn't occurred yet (i.e.it's in the future), you will mistakenly unpublish your post and put it back to draft. I have done this by accident twice.
Not to worry if you do this. Just go back and edit the time and resave.
2. DO NOT DO THIS IF YOU HAVE DATES IN YOUR URL. If you do, you will break all the links. (i.e. your links on Google, internal links, backlinks and all social media links).
If you do have dates in the URL, you should know that it is impeding your SEO and preventing you from doing this step.
INSTEAD, you should get this issue fixed for your entire site today. And, then you'll need the whole site redirected (and not w/ a plugin). It should be done at global level.
If you need someone to do this, I'd recommend Grayson Bell. He does this all the time and you'll have peace of mind it will be done correctly and quickly. I believe it only costs $47. He has done for over 60 of my clients and friends. Nothing but rave reviews. He is my go to guy for all things tech.
What about just "Republishing?"
Just republishing and changing the date won't help you with Google. Google is smarter than that. They will compare the content vs last modified version and see there's no difference.
And, just republishing to move it up to the top of your homepage won't really have any impact either. For most sites, only 1-2% of your traffic goes to you home page.
If you do want to do this, you can, but don't expect to see an SEO bump just from that.
BUT, if you decide to add more pins and/or publish more social media updates, this can help drive more traffic. And, the updated date may help a bit with your click through rate. (Note Read the Pinterest Lesson in the next section for a neat little hack on this.)
Just recognize that the bump you're getting is from all the actions you're taking on social media.
And, of course the best option will be to optimize the post, change the date AND optimize the off-page signals. (Go big or stay home.)