Back links are the life line of SEOs who want their sites to come up on top of SERPs or search engine result pages. There are a lot of advantages of having back links to you blog which are stated below.
1. Traffic:- When you have links to your blog from other blogs or sites you will get more traffic if the anchor tag of your links are attractive or matching the content of the page that posts you link.
2. Page Rank:- Google has a trademark technology called Page Rank that is the numerical measure of you page's importance on world wide web.So when more and more site/pages refer your blog your page rank increases too. The higher the PR of the referring site the better it is for your blog.
3. SERP:- Lots of quality back links will ensure your blog and its pages feature on the top of all results for a given key phrase.
4. Revenue:- In case you are using some advertisements on your blog or selling some products or referring some products then because of all the three points mentioned above you will get a huge revenue.
Now some negative things that could happen.
If your linking to some site or providing backlinks then make sure the sites to which are proper and not black listed by search engines as bad neighbourhood. e.g Link farms.