1. Brand Building
An influencer's mastery and credibility can really influence you and your blog, leading to building a brand. If they link to your blog, and they eventually share your posts on social media platforms, tweeting and retweeting your posts, it would be a pointer to their followers that you have an information portal that is worth visiting.
Note that influencers understand their degree of influence in the online world and they would be so selective about which blog to link to and which blog never to link to. If an influencer discovers a lot of typos and blogging heresies in what you write on your blog, you will destroy the relationship you've been building with him so far. He won't share your posts neither will he tweet nor retweet any of your posts.
2. Boosted Traffic
When a big-time influencer links to your blog through one of the posts on his blog, videos, podcasts or social channels, the connection can dispatch an ample flow of traffic to your own blog.
The greatest way to achieve this from an influencer is through your guest posts that they published on their blogs. You can drive hundreds of thousands of visitors to your blog. And this is a great way to build links back to your blog in due time.
And with the links you'll be getting back to your blog over time, you will build your Page-Rank and drive unlimited traffic to your blog in a lifetime.
3. Worthwhile Relationship
You never can tell where the connections can take you in the nearest future. Influencers work to a certain stage in life when they will begin to look for other people to partner with. And they can't partner with who they didn't know. And this is the reason you must build strong relationships with influencers in your niche.
While reaching out to influencers to start building bonds, make sure to connect only to the niche-related ones as you can only get high-quality links back to your blog this way.
A fascinating thing that may happen after a few years of building bonds with the niche-related influencers is that you may be given a fraction of their earnings based on freelancing as they may need your help in that area.
They would have grown their blogs so large that they wouldn't be able to continue alone to satisfy their readers' appetites for high-quality and informative content at all times. And, so, they will need someone like you having built a strong relationship for a long time with them to handle a fractional part of their business.