AutomaticTyping, sometimes called LatentTyping, is any language typing system which requires little or no type annotations (type declarations of variables, object members, function arguments) to function. Opposite of ManifestTyping (wherein type information must be provided by the programmer).
A Google search seems to suggest that this is not a commonly used term -- the only hits that use it in this sense are http://skaiste.elekta.lt/Books/O%27Reilly/Bookshelfs/books/webdesign/action/ch02_04.htm (about ActionScript) and on this Wiki. LatentTyping is essentially always used as a synonym for DynamicTyping.
Rest of content moved to ImplicitTyping, which is a much better name for this.
"Automatic typing" also refers to the habit of typing a particular word which starts with a given prefix by default, which surfaces as a strange sort of typo when you meant some other word and didn't notice. E.g., I have heard the complaint from a Usenetter that he would automatically type "linux" when he meant "lines".