Well, SEO (Search Engine Optimisation) is a process aimed at garnering the largest possible amount of traffic to your website. The benefits of which can be seen in your ranking in Google and simply the amount of eyeballs that see your business offerings.
You'll likely hear people talking about SEO however, it is actually a part of the larger category of SEM (Search Engine Marketing). SEM is internet marketing involving bolstering visibility in Google via optimisation and paid advertising.
Some of this is achieved by paying Google (and others) for better results, and some is achieved by following best practice in regards to the construction of your website and use of keywords.
This can be a complex and ever-changing area of business. An SEO and SEM professional can help you navigate these things to both save you money and make sure you get into the top pages of Google.
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