TFTP (Trivial File Transfer Protocol) is a protocol used to transfer files across a network. As it uses UDP (and no authentication) to transmit data only suitable for reliable LAN connections, it is less robust than FTP, which is used across the Internet and employs the more reliable TCP for transfers. TFTP is mostly used for booting a disk-less computer (and getting the kernel from the network) or transferring configuration files to routers. Booting over network is typically done using PXE.
To test if your local tftp server is working, you can try a command like
tftp localhost -c get filename
If you get
Error code 1: File not found
You know that your tftp server is working, but the file is not found. If your tftp server is not working, you will see a
Transfer timed out.