Why are available frequency of light continuous ? I keep hearing that atoms absorb (and emit ) photons of particular frequency which correspond to their energy levels of their electron. Where do all other colours come from ?
I think I see two questions in your post.
Each frequency of light will produce a color response in the brain. However, the brain is capable of perceiving colors that do not correspond to pure frequencies, for example pink, cyan, and brown. These are produced by combinations of frequencies which the brain boils down to a single color.
The statement that atoms absorb and emit single frequencies is only approximately true. If you could completely isolate an atom from any other interaction, and be made to be stationary (and isolation can very nearly be accomplished experimentally) it absorbs and emits light at very nearly a single frequency. In fact, even an ideally isolated and stationary atom will absorb and emit light in a range of frequencies, although that range is very very small for the isolated atom.
But atoms are rarely isolated. They find themselves in environments with lots of neighboring atoms. In a solid there are atoms nearby which distort the energy levels of the isolated atom, causing the frequencies of absorption and emission to broaden enormously. In a gas, atoms are not stationary, causing Doppler shifts as @jhobbie mentioned. Furthermore, they are constantly colliding with other atoms, which also leads to distortions and broadening of frequencies. In effect, in such cases, we have a situation where each individual atom finds itself in its own particular environment, and can absorb and emit at it's own peculiar frequency ... and there is an enormous range of such environments, so there can be an enormous range of frequencies.
Additionally, most materials when heated emit a continuous spectrum of frequencies due to the random collisions and vibrations of their atoms and electrons. The incandescent light bulb is a perfect example of that. It emits light at all visible frequencies.
There are several mechanisms that lead to random shifting and broadening of spectral "lines", so that in practice, all frequencies are available to form colors.