Here are some common reasons given for automated testing:

• Reduce bugs
  • Confirm nothing breaks when platform and dependencies are updated.
• Provide documentation
• Improve application design
  • Expose design flaws; "architectural pushback" (AiA)
  • Defer design decisions (Metz)
  • Write decoupled code (Martin)
• Support refactoring
  • Supports increasing abstractions (Metz)
  • Confidence to drastically evolve the app (AiA)
  • Clean messy code so you aren't slowed down by it anymore (Martin)
• In all of the above, the ultimate goal is to reduce costs of time and money (Metz)

Sources:

• Adventures in Angular podcast, episode 25: Testing with Ward Bell.
• Uncle Bob Martin, Architecture: The Lost Years (video)
• Sandi Metz, Practical Object-Oriented Design in Ruby, chapter 9.