1. The code $HOME is an environment variable, which represents the home folder of the currently logged-in user. (That's the one in the home directory)
2. The code of $HOME/bin refers to the bin subdirectory under the main folder, which represents the internal subdirectory of the folder. (Note the one that is not the root directory)
3. The code of PATH=PATH:HOME/bin is to set the PATH environment variable, which is to set the environment variable with the equal sign. First of all: the colon is the separator. Remember that there is also a PATH environment variable on Windows, and the separator between Windows paths is; semicolon.
4. PATH:HOME/bin means that on the basis of retaining the original PATH environment variable, add the path HOME/bin as the new $PATH environment variable. There are many variables in the computer, mainly used in the management of system files.