Directly: It adds rich content to your posts (video's, audio, images). It adds keywords in the image alt attribute and image description. Good images will increase your ranking on Google Images.
Indirectly: If the images contribute to the topic/post (not merely decorative), then you get more user satisfaction, which will increase repeat visits, word-of-mouth and links.
Do the all-things-equal test: Two pages on the same topic (let's say 'Bonobo Monkey'), but one has a picture of the topic. Which one would you find more useful? Two pages of equal quality, yet one has a picture of the author with rich markup next to it, which one would you find more credible?
As with all things, don't overdo it, or use it to manipulate: Adding images when they don't make sense for the topic, copying all your images from elsewhere, spamming the alt attribute with keywords, put a page full with unrelated images etc. Basically do not treat it as an SEO technique, treat it as enhancing your content with media to increase overall quality and user satisfaction.