The text on an image can be read by Google, yes. Thbs, it doesn't "necessarily" affect rankings. It just does what other text elements on the page does. If someone searches for your page using the text on the image, and you have a lot of ranking power,l for that page, it will show up top. Text on an image doesn't do anything special.
EDIT: I see another comment disagreeing with what I said. Google CAN READ text on an image. I snapped some meeting minutes paper and posted on a blog. After a month, they were ranking for some queries that are verbatim what's on the snapped paper.
You can actually copy text on an image in the internet by using Google Vision or whatever they call it.