The first bus appeared in France in 1826. It was called a voiture omnibus or a “carriage for everyone”. A good way of putting it. In English this was shortened first to omnibus and now it is just plain old bus. A bus is sometimes called a coach.
A bus goes along the road from one bus stop to the next. At each stop you can get on or off the bus, paying the driver. The stops that a given bus serves are fixed and it spends all day going from one stop to the next. If you miss the bus, you can wait at the stop for the next one to come along.
Most buses have stops just in one city, but some buses go between cities and some, like Greyhound, go clear across the country.
A bus, however, does not give you the freedom of a private car: it only goes between its stops. It is, however, a lot cheaper than a car and makes sense if you are always going to the same place every day, like work or school. If you live in a city with a good system of buses then you might be able to get by without a car at all.
I take a bus to work. This saves me money by not having to get a second car for my family. It also allows me to sleep or read or write instead of driving.
Current buses are like a large room on wheels. The room has many seats and large windows. Most buses seat between twenty to sixty people. The bus has a motor built in that gives it enough power to move fifteen times faster than someone on foot.
What makes a bus a bus is not how it looks or how it is made or how it is powered — the first buses were drawn by horses, after all. What makes a bus a bus is the sort of service it provides.