External ADC Vs. Internal ADC
Usually the kind of ADC integrated on-chip within a microcontroller, is typically a capacitive charge-balancing successive-approximation type (SAR), and usually no more than 12 bits resolution. Sometimes a bandgap reference is included on-chip, but often they just measure ratiometric to the digital power supply -- so they are low accuracy, no point in going with higher resolution. 

The typical 12-bit microcontroller-integrated ADC is adequate for lots of general-purpose applications (like most Arduino/hobbyist stuff and even some industrial applications), but higher-end applications require more specialized ADCs. 

Some motor control schemes require simultaneous sampling on multiple channels; can't do that with on-chip ADC.

Weigh scale applications typically use a Delta-Sigma ADC. Despite the low output data rate, they often use oversampling to reject 50Hz/60Hz powerline-induced noise.

Capturing sound at decent quality requires a moderately high-speed ADC (CD audio sample rate is 44.1kHz, DVD audio sample rate is 48kHz). A typical microcontroller's on-chip ADC doesn't go that fast, and its resolution is too limited -- some may be able to get old-timey "telephone quality" sound adequate for voice, but the distortion is somewhat objectionable.

Video frame buffer capture requires a very high-speed ADC. So does a digital sampling oscilloscope. And RADAR and specialized imaging applications require very, very high-speed ADC. 

Medical equipment requires high precision ADC, with noise rejection. For example an ECG (electrocardiogram) must sense very fine details of the heart rhythm, on a set of electrical signals that are significantly less than the 50Hz/60Hz powerline-induced noise from electrical wiring in the room with the patient. 

So yes, there are a lot of applications that can work just fine with the cheap 12-bit on-chip ADC using VDD as the reference -- for those applications, you're absolutely right, it makes sense to just use the on-chip ADC if it's good enough. That's why it's there. But there are times when more performance is needed.