FTP stands for File Transfer Protocol.

A protocol is a set of standard commands and responses that computers use to talk to each other. Other examples of protocols are:
POP3 Post Office Protocol (version 3) - used to retrieve email from a mailserver
SMTP Simple Mail Transfer Protocol - used to transmit/send messages
HTTP HyperText Transfer Protocol - used to view web pages

The File Transfer Protocol includes commands like GET and PUT which are used to transmit files to and from servers. A computer which contains files that can be accessed by FTP is often called an FTP server, or FTP host.

When connecting to an FTP server you need to know it's hostname. The hostname is a combination of words in a particular order which is translated (behind the scenes) to an IP Address, sort of like a phone number.

Example Hostname: ftp.mywebhost.com

Example IP Address: 192.17.105.212

As you can see, the hostname is easier to remember and communicate to others. An FTP program can use either the Hostname or IP Address to connect to the server.

FTP programs, often called clients, are used to simplify the use of FTP for the end user. Rather than issuing commands one after the other at a command prompt, you can use an FTP client to manipulate and transmit files via a GUI (Graphical User Interface). This means that you can drag and drop files with your mouse and your FTP client will issue the relative commands to the server behind the scenes.