Tilde expansion in bash means the shell looks for a tilde character at the start of a path and replaces it with the user's home directory path. For example, when you run 'echo ~', the shell changes ~ to '/home/username' and prints it. Similarly, 'cd ~' changes the current directory to the home directory. This expansion only happens if the tilde is the first character in the path. If the tilde appears later in the path, it is treated as a normal character and not expanded. This behavior helps users quickly refer to their home directory in commands.