I'll try to explain this as best I can, but it may not be perfect..
Well a few things, some not so obvious. A brushless motor is not simply a motor "without brushes". On a brushless motor, the positions of the magnets and coils are reversed. To accomplish rotation, the magnetic field of the coils that are now positioned on the outside need to be changed - quickly... to achieve this, the motors are AC powered (instead of DC) and they need to be controlled digitally.. digital control over AC power allows the fields to switch between + and - instantly. this eliminates the need for a physical connection to transfer current to what's rotating, which is what brushes do. With an brushless motor, there is no need for them.
Brushes do wear out. I've had to change them on my old dewalt drill years ago. They are easy enough to change, but they still produce friction and heat - those are both a parasite to a motors efficiency.
So what do you gain - the lastest technology in cordless tools. You should get about 10% longer runtimes, and in theory - longer motor life. You also get a tool that's digitally controlled, with built in overload protection... where an old brushed drill will chug along straining to do something it should not be doing - the digital controls will (should) shut the tool down before something burns up. As a note, the brushed m18 tools also have overload protection. If something draws too much current, or a wire gets too hot, it will stop the tool. Video demo posted below..
In its simplest form, older styled brushed tools were just a DC battery, running though a trigger that was simply a dimmer switch, and then to a DC motor.. brushless tools are a big step forward, and brushed tools have come quite a ways too..
All that said - brushless does not always mean a tool is more powerful. It simply means it uses a different technology.