As I understand, in a balloon/air balloon, a gas burner is used to heat air or using some lighter atom like helium. Since helium or hot air is lighter and less dense than the cool air around the balloon, the heated air or helium causes the whole balloon to rise. And as I understand, vacuum is a space where there are no atoms inside. So no atom inside means it's lighter than to have atom an inside? Isn't it? So why we can't make something fly by giving it a vacuum container?
I assume you are asking why we are not drawing air out of a balloon like container so as to create the lower density that helium or hot air gives us.
The answer is that it is hard to maintain a vacuum with a thin enough, so as to be almost weightless, rigid contaning surface. A balloon with gas inside equalizing the atmospheric pressure with the gas pressure is easy to make air tight and stable. A vacuum in a thin enough walled container would be liable to collapse, due to the atmospheric pressure, and would be hard to make air tight.
Yes, creating a vacuum container and flying it is possible. But the efficiency would't be any greater than helium balloon. When a vacuum is created, a low pressure tending to zero is created. There will be high pressure outside the container or balloon. This pressure will start squeezing the container. The container must be strong enough to sustain such high amounts pressure. This would be like building a submarine. The vacuum container would have to lift itself (which would be several times heavier than a balloon) along with a pay load.
In 1670, not long after the time of Galileo & his studies of air pressure, Italian aeronautics pioneer Francesco Lana de Terzi published an idea for a vacuum-balloon-based flying airship supported by four evacuated copper balloons. However, at that time they didn't have the technology to create a vacuum, and an evacuated balloon made even from the strongest known metal alloys is easily crushed by atmospheric pressure.
In theory, another option is to use radiation pressure to inflate the balloon with photons. But this is impractical, too. It takes a radiation flux of around 15 terawatts per square metre to produce the required pressure ($\approx 10^5$ pascals), which is rather intense. ;) The interior surface needs to be highly reflective, and any energy that's not reflected is lost as heat. So the balloon needs a substantial power source to inflate it and keep it inflated. Note that 15 terawatts is roughly 40 times the combined capacity of all of the nuclear power stations in the world.