If you are trying to build traffic to your website, especially return visitors, you need:
1) An opt-in process, and a quality newsletter (a reason to sign up in the first place).
2) Monthly newsletters with something of value . . . you want subscribers to want to read the newsletter, so a compelling headline and something of value inside is necessary.
3) Content in the newsletter can be "teaser" or summaries, that lead back to your website.
Most websites will offer a newsletter, but the information n the newsletter is not that valuable, so the subscriber will ignore it after the first issue.
I do NOT advise buying lists from online resources who claim they have opt-in addresses to different target groups. You can get some traffic doing this, but it will result in a lot of bounces from your website. However, if you buy ad space on someone else's email newsletter that has potential customers in their readership, that can bring you some targeted, pre-qualified traffic.
When building your own list, offer something of value and bring readers back to your website for more information or offerings, that will generate website traffic. Another approach is to build a set of autoresponders so readers can sign up for a 10 week mini-course, where the visitor signs up and you have a set of pre-written, useful newsletters, which also have prominent links back to your website. If professionally done, this can be very effective.
Blogs can do the same thing or can blend both content and emailing together. I recently set up a Wordpress blog for a client which they use to push more customers back to their online store. Customers subscribe to the blog, so they get notified and the new blog article gets pushed out by email to the subscriber.
Lastly, you really need to have quality website content so visitors will want to come back to your website anyway; the newsletter is just a nudge.