The answer is in three pieces of security provided by the website's structure: References, Vouching, and Verification. Together, these things make couchsurfing just as safe as (or safer than) any other method of travel. These items are all listed on every couchsurfer's profile. The goal of listing them is to make couchsurfing more like staying with a friend of a friend than a complete stranger. Every surfer has an online profile much like they do on Facebook-- pictures, listed interests, a bio, lists of other couchsurfing friends they've connected with. So before you meet the person, you know a little about them. But it also has these three items that you won't find on any other site.
References- Anyone who meets, stays with, or hosts any couchsurfer can write a reference on that person's profile, listed as either positive, neutral, or negative, categorized as to whether they were a guest, host, and/or travel buddy, along with comments. When someone writes you a reference, it appears permanently on your profile-- you can't edit or delete it, only the writer can do that. If someone was a great guest or host, they'll have a lot of positive references. If they steal and break things, or put people in uncomfortable positions, they will have negative references. If you see someone who has a negative reference, it will be featured prominently on their profile. When you have negative references, it becomes hard to surf anywhere or host people, so you always want to do you best to get positive references. Conversely, if you find someone who has a negative reference, always read the comment section to see the reason. Sometimes people leave negative references for reasons that might not affect you (miscommunication, personality clashes, etc). and it is up to you to decide whether it is really a red flag or not.
Vouching- A vouch is an icon you see at the top of someone's profile, once some other user has "Vouched" for them, saying they have complete and utter trust in that person. Here's the thing that makes it special: you can only vouch for someone once you yourself have been vouched for by three different people on couchsurfing.org. Each of those people in turn must have been vouched for by three different people, etc, etc. Anyone who has been vouched for has made deep connections in the couchsurfing community, and is known and trusted by those around them. Ideally you should only vouch for someone who you have both hosted and been hosted by, but failing that, just make sure it is someone you trust-- once you vouch for them, anything they do is reflected back on you.
Verification- It's the first and easiest step you can do, because you can do it by yourself. It's a three step process that leads to yet another prominent icon on your profile. The first step is locking in your name and physical address. Once you've done this, the couchsurfing team will mail you a postcard with a code on it. When you get it, you will enter in the code to verify you live (or at least get mail) at this address. This is the bare minimum of verification. The functionality of it is that in the unlikely event that any sort of legal complaint is lodged against a user, the local authorities can at least track them down by physical address. The last step to Verification is optional and only really shows dedication to the concept of couchsurfing- a monetary donation.
Now I know some surfers who object to this donation on principle-- they say that every other aspect of couchsurfing is 100% free of charge and always should be. But creating and maintaining a community that has more users than Facebook had just a few years ago costs an enormous amount of time and money. Since couchsurfing.org has no advertising anywhere on its site, donations are its only source of revenue. I say they've earned it. It's a different amount depending on the country you came from, but it's almost always about the price of one night in a hostel dorm bed in your country (Americans for example pay US$25). It's well worth it.
Together, with the fact that all messages through couch surfing are recorded, these safeguards make the backbone of couchsurfing security and should be the first things you look for when considering any potential host or surfer.
Speaking of looking for surfers, here's a special concern for those wondering "is couch surfing safe for women alone?" First of all, yes, it is. More than a million women are on the site and have had no problems. But if you're still worried, I would like to point out that you can be very specific in your search by gender, age, keywords (good way to find common interests), and specific location. A lot of women tell me they wouldn't feel comfortable staying with a strange man they don't know. Simple answer: restrict your search of hosts to women only.
If you want to read further, I recommend what couchsurfing.org has to say on the subject themselves.
Up next, Tips for surfers, followed by tips for hosts.