Why does coffee from cafes taste better than coffee made at home?

Good question. Making great coffee is technical. There are a number of advantages that a cafe or coffee shop has over coffee being made at home.

Grinding:
A coffee made in a cafe will grind the beans right before the coffee is made. Coffee oxidises once it is ground and becomes stale. Freshly ground coffee beans make better coffee.

The consistency of the grind is also important. Most cafes (in the UK at least) will be grinding for an espresso coffee base or for a drip feed. These both require a fine grind of good consistency. A better grinder will produce better coffee.

Brewing:
A cafe will mainly be producing expresso as a starting base (for espresso, latte, flat white, cappuccino etc). Espresso machines brew under pressure. The process requires the right amount of coffee, the right tamping technique, a good machine and a good barista to get a great shot of coffee.

Good espresso machines are actually really expensive. A cafe is going to have a better machine and better technique.

Roasting:
Many cafes now roast their own beans or source directly from a local roaster. The time between roasting and brewing is important. A cafe will have much more control over this time period due to the volume of coffee that they are making.

Beans:
Coffee shops spend a lot of time sourcing the best beans or finding the best roasters to make the best coffee. They will be spending more on the beans than a typical household or benefiting from economies of scale.

So basically: better equipment, better ingredients, better technique and a more timely process for what is actually a fairly scientific process.

Also I always find coffee tastes better if someone else is making it and you don't have to do the washing up!