First of all, great work. It looks like you boosted your conversion rate from 0.19% to 0.43%. Which is a 125% improvement, or with confidence intervals, 55% - 179% improvement.

However, before everybody goes out and puts puppies on their homepages, they need to realize that there are a bunch of things being tested.

Image vs. no image: Is it possible that having any image at all improves the conversion. You should test with other pictures: perhaps some animals, people, nature, and see if the puppy is what makes it work.

Call to action: The 'puppy' version also features a more succinct call to action in "Sign up now" rather than "Start your 30 days free trial." Perhaps this also contributes some of the difference.

Button size: The button size in the 'puppy' version is smaller. Perhaps this has some effect as well.

Length of text: The 'puppy' version has more description of what is involved in the free trial. It says "Pick a plan & sign up in 60 seconds. Upgrade, downgrade cancel at any time." vs. the no puppy version that says "Start you 30 days free trial."

Vertical vs. Horizontal Layout: The 'puppy' version has a vertical layout of the text and button, where they are stacked on top of each other rather than left or right.

So there are at least five different changes made between these two designs. Clearly the second design wins on conversions, but it's not entirely clear to me why it wins.