Try:

Intent intent = new Intent(SplashScreen.this, MainActivity.class);
startActivity(intent);

Try:

// create an intent for a specific component - your main activity
// your activity need to be also described in your manifest xml
Intent intent = new Intent(SplashScreen.this, MainActivity.class); 

// tell os to display new activity (which one is described in the intent)
startActivity(intent);

Edit: Added comments