How will using affiliate marketing programs on my site benefit my blog?

It's very important for quite a few reasons,

1. CEO, The more you use guest blogging to spread backlinks to your blog the better your chances of getting higher CEO rank.
2. Blogger reputation, This is mostly personal, when you have a number of guest posts on other websites your digital footprint becomes wider which is better exposure for you and for people who look you up and end up on your blog.
3. Content marketing, If you're monitizing your website, more traffic means more clicks, means money.
4. Building a community of bloggers who help promote each others blogs and content is very important for traffic, marketing and online reasons, having a community of other bloggers that you can work with helps accelerating the rate of growth in general.

And many others, these the ones I can think of right now. Hope this helps :)

Monetising one's blog is an important thing. But first and foremost develop your blog's reader base. It is very crucial that you need to be seen as an expert and a trusted authority in your domain. People will spend only when they trust you.

Consider affiliate programs only when you feel your blog has gained respect and achieved a considerable following. Also make sure your affiliate programs are relevant to your blog's content. Make sure affiliate programs primarily benefits your readers first and then you. 

People can see through a site/blog which is tyring 

Affiliate marketing programs are very important for any blogger who wants to montize their blog. Make sure what when you are looking for Affiliate programs to promote in your blog to select program that are related to your topic. For example, if you have blog about weight loss, youw ill get a high conversion if you are promoting weigt lose products.

Affiliate marketing programs can be considered as extra sourcem of in come beside google adsense