Search engine optimization allows you to optimize your website and get the traffic. The search engines have complicated algorithms. The search engines use these algorithms to rank the websites. The search engines crawls the web pages and checks for various things. Few of them are:

Incoming links: the search engines check for the incoming links to a page when crawling. This is a major factor which contributes to the ranking of the website. The Google has clearly told the webmasters in their documentation to increase the number and quality of the incoming links in order to get better ranking.
Content and keywords: content is the most important thing. It has to be relevant to the website and it needs to be fresh. Anything which is not unique and is copied from the other online sources, will be immediately spotted by the search engine bots and will make negative impact on your ranking. The keywords are also very important. You will have to make sure that you are using the keywords with the proper density. If you over do this, your content will be considered as spam. If you under do this, your content will be considered as irrelevant to the particular set of keywords. This means that you will have to check the keyword density.
Other various factors: there are many other factors which the search engines look for while crawling. These include the easy access to all the sections of the web page, easy to read content, meta tags etc.

Now that you know what the search engines look for, you can work to improve them. But how would you do these things if you do not have tools for them? Take the example of keyword density. Is it possible for you to calculate the keyword density of the entire content without a tool? Can you read all the content and highlight the keywords and then make the calculation to determine the keyword density? I do not think so that any one can do it with so much content connected to every website these days. You will have to use the tools for this. You will find tools for every task and the only thing which you will have to do is to learn how to use the SEO tools.