It means that if your speech is written in the way you casually speak, it's easier to remember it (since you'll not have to remember fancy words or turns of phrase that you wouldn't normally use). The idea being that it's easier to remember or reconstruct speech that comes natural anyway.
It will also be easier to improvise and fit the tone if you forget what you were supposed to say.
Aside from the above, which are about memory, it's also good for making it natural: you'll sound more authentic/natural speaking as you normally do, than trying some fancy speech, and it will also be easier to add off the cuff remarks that also fit the tone, like an idea that occured in the moment, or to respond to something that happens just before/while speaking.
It will also be easier to improvise and fit the tone if you forget what you were supposed to say.
Aside from the above, which are about memory, it's also good for making it natural: you'll sound more authentic/natural speaking as you normally do, than trying some fancy speech, and it will also be easier to add off the cuff remarks that also fit the tone, like an idea that occured in the moment, or to respond to something that happens just before/while speaking.