bash – What is the command (chmod + x $ 1) in the terminal?

The command chmod is used to

change the file mode bits

            The format of a symbolic mode is  [ugoa...][[-+=][perms...]...],  or
perms is zero or more letters of the set rwxXst, or only one
ugo set letter. Several symbolic modes can be given, separately
evaluated by commas.

(of man or reference manual page for chmod).

The + x tells chmod to set the parameter perform (or search for directories).

The $ 1 is usually used in scripts to designate the first parameter passed to the script. ($ 0 refers to the script itself) however if a shift has been executed, the parameters may have changed, so it is the first one at the moment of execution.