Enabling passive mode
In most cases, you should be using "passive mode" to avoid network problems.

These instructions explain how to turn on passive mode for FileZilla (version 3.1.6) for Windows, although other versions are similar:

Start the FileZilla program if it isn't already running.
Click Edit, Settings in the menu bar. The "FileZilla Options" window will appear.
Select Connections, then FTP on the left hand side.
Choose the Passive (recommended) option.
It should look like this:

After you've made the changes, click OK to close the window, then try to connect and see if it has solved the problem.

Choosing active mode instead
Although it's very rare, we've also heard of a situation where you need to use "active mode" instead of passive mode. In particular, you may need to do this if you see a "Software caused connection abort" error message.

Just follow the steps above, but choose "Active" instead.