In passive mode, the client has no control over what port the server chooses for the data connection. Therefore, in order to use passive mode, you’ll have to allow outgoing connections to all ports in your firewall.
In active mode, the client opens a socket and waits for the server to establish the transfer connection.
The fix is to use active mode
FileZilla uses passive mode by default, but due to the network configuration of certain servers, active mode is required to establish a data connection. A bit of background reading with some explanation is farther down.
In FileZilla, click on Edit | Settings.
Under Connection, click on FTP and choose Active as the Transfer Mode.
Under Connection, under FTP, click on Active mode and choose “Ask your operating system for the external IP address” (the default setting).
Under Connection, under FTP, click on Passive mode and choose “Fall back to active mode” (this is an optional setting).
According to the FileZilla wiki page on network configuration:
In passive mode, the router and firewall on the server side need to be configured to accept and forward incoming connections. On the client side, however, only outgoing connections need to be allowed (which will already be the case most of the time).
Analogously, in active mode, the router and firewall on the client side need to be configured to accept and forward incoming connections. Only outgoing connections have to be allowed on the server side.
In passive mode, which is recommended (see below), the client sends the PASV command to the server, and the server responds with an address. The client then issues a command to transfer a file or to get a directory listing, and establishes a secondary connection to the address returned by the server.
In active mode, the client opens a socket on the local machine and tells its address to the server using the PORT command. Once the client issues a command to transfer a file or listing, the server will connect to the address provided by the client.