I took a class, back in my college days, that taught how to use Excel. At one point in the class, they taught us how to use some Basic programming languages within Excel. It was a really basic assignment, just making Excel pop up a window that said "Hello". I had taken a programming class earlier in college that taught me some pretty good basics in the Java language, so programming in Basic and doing this particular assignment took me no more than five minutes. On the day the assignment was due, however, I noticed a couple other students desperately trying to finish the assignment before class started. They told me that they had spent a couple hours trying to finish it, and seemed like they never wanted to look at code again. Once I got over thinking how much of a genius I was, I started to reflect on why it was so hard for some people to understand programming languages. What in the world does this have to do with SEO? More than you'd think. Understanding how computers work could help you design your site to speak better to search engines, and show up better in search results.
Computers, as smart as they are, are incredibly stupid. They have to be given precise, exact instructions in what to do. It would be like asking someone to get the milk in the fridge and telling them the precise distances they needed to travel, the exact angles they would need to turn, how to open the fridge, where the milk was located, telling them how to grasp the milk with their hand, etc. Imagine having an employee where you had to relay each instruction exactly. They might last a day before being given the boot.
Now apply this with search engines. How do they decide if a site is relevant? With a LOT of instructions. Someone taking a basic programming class (like me) wouldn't be able to come even close to the complexity and functionality that we see in most of today's modern search engines. As a result, the decision on what site is relevant comes down to simply mathematical equations. Yes, they're very complex mathematics that continuously evolve, but it is still math.
With that understanding, how does your site do in speaking to the robots? Does it place the keywords you want them to find where they expect to find it? If you're not sure, try this simple tactic to see what the search engines see. Do a Google search on your name. Underneath your website's link, you should see a small green link that says "cached". Click on that, and you will see a copy of your site that Google has stored. At the top of the page, click on "Text-only version". This is it. This is what search engines are looking at on your site. Does your site still have a clear message?
Now let's start thinking like a search engine. Since the search bots can't actually read, it becomes a numbers game. Let's take two sites of the same industry (let's make it a tax software site since we're in that season). If site A mentions "tax software" 2 times on their home page, and site B mentions the same word 20 times, which is more likely to be about tax software? All other things being equal, Site B will most likely appear first. We can apply this to other aspects of the site too, such as the number of links to the site, the amount of keywords that they have in H1 and H2 tags, or bold words.
Before someone goes out and starts packing in keywords on their home page, however, I must make a disclaimer. Google is very good at catching people trying to manipulate the system. If you put your keyword 100 times on your home page, when other sites on the average mention the word only 20 times, it will throw red flags. You want to think like a search engine, but still write to humans.
As Google continues to improve it's algorithm, and continues to improve the results they bring to site searchers, it will feel less and less like automated programs are the ones generating the search results pages. The fact that programs and search engines are able to mimic human behavior so well already is nothing short of extraordinary. But, for now, it's still programs looking at your site, and it's still a lot of math.