Google has made recent changes that encourages all users to start sending their website through a secure channel, using SSL (Secure Socket Layers). Currently most websites (including my own), are (or were) unsecured websites. The delay for most of us usually involves the fear that securing our website will reduce page rank, and effectively lower our visibility after years of of optimizing a website for search engines. Since SEO is such a concern, many of us delayed the transition for as long as possible, even if that meant keeping an unsecured website. That doesn't mean the website isn't secure on the back end, it means, for our visitors, they will get a message that they are not secure for them to submit information. So securing your website is basically helping to protect the general public from hacking attempts.
Since SSL provides a level of security to protect customers from hackers, it obviously should have been a standard years ago, but it wasn't. Google is trying to change all that. It used to be a requirement only for websites with shopping carts, but that has been changing the past year, especially due to the increases in attempts to hack websites. See this video from CNN about this change on Google.
The "http" stands for HyperText Transfer Protocol, and Google has been encouraging websites to switch to "https" which adds "Secure" to the end, which means the website tells browsers and users that you have a "secure" website that is safe to send information on. Up until this year, it has only been a suggestion, but Google has been making a push for it lover the past few years, and this year in particular, is the time when sites should be compliant. It's not required, but I recomend doing it.
As of today (March 8th, 2017), our website has been secured by an SSL certificate and includes the "https." In fact, you can't get to our site any other way, as it automatically forces you to go to our secured server.
The pro's for securing your website are better search engine optimization over the long term, and a secure website. Also, as things are changing online, websites that are unsecured will start showing errors, signalling that the customer is not on a secured website, which in term, reduces your rank on Google. Since SEO and page rank is such a big concern for all businesses on the internet at this point, it's obviously something we want to take serious; including the negatives of securing your website.
The con's are temporary, but are not very pleasant. This includes a short term reduction in rank, and requires more extensive SEO just to get where you were prior to the change. Over the long run, your rank will actually improve, but because your website will switch from http://www.yourwebsite.com to https://www.yourwebsite.com, it's actually similar to a change of address on the web. Most people don't know that even the "www" and "non-www" links to your website are considered different addresses also.
In my experience, it does indeed hurt rank, and as of today, having had SSL enabled for the past few days, it has hurt my rank fairly significantly. That being said, knowing what I know, and taking the risk for our website, should demonstrate the importance of taking the leap. If you want to read more about SSL, here is someone at Google explaining more about it.