The subscription model is what most of us are used to. A journal publishes articles that authors have submitted. Those who advertise in the journal or those who purchase a subscription to the journal, either in print or electronic format, cover the costs of publication. If an individual wants to gain access to a specific article, the journal may charge a fee to purchase that article. The information in the journal is not available otherwise.
The open access model is a newer model and has become popular as the internet has gained popularity. A journal publishes articles that authors have submitted. Those who publish in the journal cover the costs of publication through publication fees. Articles that are published in an open access journal are freely available to the public with no subscription fee, although they may need to create a free account with the journal publisher so they can track usage data.
The combination model is just what it sounds like. It combines the subscription model and the open access model. An author who submits an article to a journal has the option of choosing whether to pay a fee and make the article available to the public or to make the article available only to those who have a subscription to the journal. The journal will usually make all articles available in their print journals, which typically require a subscription. They will make electronic versions of open access articles freely available, but will require those with a subscription to log into their website to access the articles that require subscriptions. Many of the larger publishers are moving to this model. Author fees for the open access option can be substantial, depending on the reputation of the journal and publisher.
If you are looking to publish in an open access journal, check with your department or your institution. They may have money available to encourage publication in an open access journal. Publications that are available to the general public and that are associated with your institution increase the institution's visibility and benefit them as well as you.