Drinking coffee at a coffee shop is a common activity, as people often go to coffee shops or cafes to get out of the house and change their mood.
Coffee shops often use better beans and brew using better methods than those you can get at home, so you can enjoy coffee that you wouldn't normally get. They also have a stylish or retro atmosphere.
They're also used as social venues. If you're drinking alcohol, it's an izakaya, but if you're not, it's a coffee shop. They're perfect for meetings, dates, and conversations with friends.