Do follow and No follow refers to links which are placed in a blog. The difference between the two types of links is:
A do follow link is placed in a blog post to (a) give a link to another post in the same blog and (b) give a link to another website which could be important and relevant to the text of that particular blog post.
A no follow link is placed in a blog post to (a) give a link to another website which may provide some further information related to your blog post but is not a high quality site and (b) give a link to an affiliate marketing program.
An example: Yours is a tourist blog. Let's say you post something about Rome and mention what is to be done if a visitor from India loses his passport while traveling there. In this case, it would be extremely helpful to give a link to the official site of the Embassy of India in Rome, Italy. In this case, a do follow link would be good.
Now suppose you come across some interesting restaurant in Rome which serves Indian cuisine. You could make a mention of it and give a no follow link to the site which has reviewed it or to the restaurant's site if there is one.
In another blog post if you are writing about a useful piece of travel accessory, you could write about it in detail and give a no follow link to the online shopping site where this accessory is available. This site would be the one where you have signed up for an affiliate program.
As for traffic, some search engines may not follow the no follow link at all.