Magento has a search function that customers can use to look for products on the frontend of your store. When a customer searches for a word or a phrase Magento creates automatically a search term entry. You can check and manage these terms from the admin panel of your Magento. To do this, after you log in go to Catalog>Search Terms.
On the page that opens there's a table with the existing search terms; these are words or phrases that have been used one or more times by customers. You can see how many times each term has been used and the number of matching results. To edit a term click on its row in the table; to add a new one click on the Add New Search Term button above the table. There are several settings that you can change/configure. These include the name of the term/query, the number of matched results and the number of uses (these two can be configured only when editing existing terms). You can also make the term that you're editing/adding a synonym of another term. This means that when somebody performs a search for that term the results of the synonym will be displayed instead. From the Redirect URL option you can set a fixed page that will be displayed every time when somebody searches by using the particular term; just type the full URL address in the field. When you're ready with the settings click on the Save Search button.
There are also some general search settings that you can configure from the admin panel. Go to System>Configuration>Catalog button on the left>Catalog Search panel on the right. You can set the minimum and maximum query length, the allowed number of words per query and the search type.