That's not MS-DOS, but Command Prompt (aka "command line", "CMD.EXE" or just CMD). They're not the same. MS-DOS has not "start" command.
There are two things you need to know here. First, a command line argument is placed in quotes if it includes special characters like spaces, |, <, > and such. Ex:
dir "c:\program files"
You need the quotes because of the space in the folder name.
However, the START command is peculiar. It has a quirky rule that if the first argument is quoted, it represents a title string for the window it will create to run the program. So, with START you need to add a title (may be empty or blank) *before* a quoted path to the executable. Ex:
start "" "C:\Program Files\Internet Explorer\iexplore.exe"
This will start IE with a blank window title. (Which IE will promptly ignore and replace with its own title.)
PS: The proper term for the type of title above is "window caption", but the bar it is displayed in is called a "title bar". Go figure.
PPS: David has it almost right, except that MS-DOS directory names could have file extensions. They weren't used often, but they were allowed.