If you engage in link building, then checking your backlinks to see if they are nofollowed is a must.
But before I go further, I have to talk a little about what "link juice" is. In the world of SEO, getting another website to link to your site is a great achievement. That link is seen by search engines as an endorsement. Search engines factor in the number of links that point to your site when they are ranking your site in their engines. "Link Juice" is a non-scientific term for the so-called power that the link provides your website or webpage in question.
Nofollows are an attribute that can be coded into a link to stop the link juice from flowing to a website. This is a very common thing you will see in the links present in the comment section of blogs.
To find out if your backlinks are passing link juice, you should check to see if the links have nofollow attributes inside them. If they do, then the link you worked so hard to get isn't doing much for you since the nofollow attribute basically tells Google to ignore your webpage.
It might be a little hard to see in the picture above, but rel='external nofollow' is in the anchor link. So, even though a person can click through on the link, no link juice is being passed.
Some people think that Google actually does count some link juice from nofollows, but to be conservative in your backlink counting, you should assume nothing is getting passed.
Google will tell you to ignore this practice, and I somewhat agree. It's kind of a tedious, unnecessary task, and your energy is better spent on creating great content instead.