By changing the mode of a file, you are giving permission to various groups to be able to read, write or execute a file.

Most use number codes for chmod commands, but those who wish to learn more can check out the myriad of tutorials out there for more advanced commands.

Each digit in the command is a binary representation of:
rwx (read/write/execute).

A chmod of 755 means:
111(7) – Owner can read write execute
101(5) – other in the group can execute or read, no write
101(5) – rest of world can read and execute, no write

A chmod of 777 means:
111(7) – Owner can read write execute
111(7) – other in the group can read write execute
111(7) – rest of world can read read write execute

When installing WordPress, some directories need to be changed via chmod. Some plugins require the /wp-content/ folder be made writeable. In some cases, this may require assigning 755 permissions or higher (777 on some hosts). The same is true for /wp-content/cache/ and maybe /wp-content/uploads/