+1 Button
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The +1 Button is a webaction button proprietary to Google+ that is essentially their version of a like button.
Google+ allows you to put a "+1" button on any page that when clicked, does a "+1" (similar to a like) of your page, inside Google+, on the Google+ profile of whoever clicked the button.
Why
Due to the diminishing use of Google+ and the removals of both search results effects, and the +1 counts from the "+1" button (see #History below for citations), it’s not clear there is any reason left to actually include a "+1" button on your site or blog posts.
- (please provide your own personal reasons "Why" if you happen to put "+1" buttons on your own site)
Instead, consider putting a like webaction button on your posts, with fallback(s) to whichever silos a post is POSSEd to.
How
(stub)
Is there a way to provide "+1" button functionality via a simple hyperlink rather than a heavy JS embed?
See also webactions for how to put service-independent buttons like a generic "like" button on your posts.
IndieWeb Examples
(none so far)
Or perhaps 
Ryan Barrett does on his posts?
Criticism
Recommends proprietary Google XML
The first example (in their docs) of how to embed a +1 button in HTML uses this proprietary XML:
<g:plusone></g:plusone>
Recommends nonsemantic DIV
The "HTML5-valid +1 tag" (thus admitting their g:plusone XML isn't really valid) example has:
<div class="g-plusone" data-size="tall" ... ></div>
History
In mid-2017, Google removed the share count from "+1" buttons.
- 2017-06-15 Making the G+1 button load more quickly
Beginning in a few weeks […] the G+1 button will no longer display a +1 count. If you’re a publisher, you can rest assured that these +1s do not affect search ranking […]
- 2017-08-08 Google+ Is Removing Share Counts: Everything You Need to Know
- 2017-09-14 Another Dead Button: Google Plus Removes Share Counts
Google IO 2013 motivation
At Google IO 2013, in the "Google+ Platform Overview" session, the Google presenters said that one motivation to add +1 buttons to your pages is that Google search results show who +1'd a post.
However, Google has since (2014? 2015?) dropped that aspect of Google search results, which no longer show who +1'd a post, whether you're logged into Google+ or not.