Basic HTML browser
If you choose the View in Web Browser action then activating a row will display the web page whose URL is in one of the columns in a web browser. You are given the option of what browser you would like to use in this case; the options available depend on your java installation.
The Basic Browser and JavaFX Browser options use an internal browser implementation that runs inside the TOPCAT application itself. This can view HTML or plain text pages and has forward and back buttons which work as you'd expect. The JavaFX variant has more capabilities and generally works better, for instance it can render JavaScript as well as static HTML, so it's generally better to select this if it's available, but it's not present in all Java Runtime Environments. The Basic variant is always available. These browsers look approximately like this:
Basic HTML browser
Alternatively, the System Browser option may be available. This will send the URL to the default browser installed on your desktop. This will certainly be a more capable browser implementation than the internal options, but there may be annoyances; for instance in some cases it opens a new tab every time a new URL is opened.