startActivity
Start an activity, like you would start an application: for instance: you have an app with a home-screen and a user-info screen: if you press the user-info button, you start the user-info activity with this.
startActivityForResult
Start an activity and expect something in return. For instance, on your user-info screen, you can upload a profile picture. You start the gallery-activity with the explicit goal to get a URI back with the preferred picture. You start this activity literaly to obtain a result (the picture. There are some techinical ways to make sure you actually get the result, but they are quite clear in the manual.