You can use a message filter.
To do that, on the top menu go to Tools > Message Filters, it will open a window where you can manage all your filters. If you are using multiple email addresses, choose the one whose messages you need to filter, and click the New button. On the following dialog you can setup the rules that define your filter. 
- Filter Name as you can guess is just a name to the custom filter; you can use anything you like.
- Apply filter when lets you choose whether the filter should be applied automatically when checking mail or manually run by you, or both.
- Match... options define when the filter will be applied: if all the subsequent conditions are met (basically a boolean AND), if any one of the conditions is met (a boolean OR), or always, without regard of any condition.
- The first white area is where you insert the conditions that the messages have to met to be affected by the filter. Its content is pretty much self explanatory: from the first dropdown menu you can select in which part of the email to look for (in your example you should choose Subject, but it could also be a particular sender, the mail body, and so on); the second dropdown menu lets you choose if the string that you will enter should be matched exactly or if it just contains a part of the text that you need to match, and finally, the text box is where you insert your string. By clicking on the + button next to it, you can add other conditions; in example, to filter all the messages sent to you by someone@somemail.com whose subject contains Hello World!, you need the select
Match all of the following, insert a first condition like thisFrom - is - someone@somemail.comand a second one like thisSubject - contains - Hello World! - The second white area define the actions that should be performed on the messages identified by the previous conditions; this one is very clear to understand too. In your case you need to select Mark as read, but you can add more actions as you wish, i.e. moving or copyng the message to a particular folder, applying a tag, forwarding it, and so on.
The Mozilla Knowledge Base has an article about message filters that you might want to read.
EDIT If you don't want the filter to automatically affect your emails, select Manually Run on the Apply filter when dropdown menu; then the filter will be executed just when you manually do so; to do this, once the filter is set up, go to the folder that you want to filter (.i.e. your inbox) and from the top menu go to Tools > Run filters on folder