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When light falls on an atom and the energy of the photons matches the gap between the energy levels of electrons of this atom, the electrons will absorb the photons to get excited to the higher energy level. This makes different things have different colors. My question is - why don't these electrons fall back to their original energy levels, reemitting the absorbed photons?

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    $\begingroup$ They do; for every absorption spectrum, there is a corresponding emission spectrum. See this link for more information. Since you are new to the site, please also note that questions (such as this one) that can be answered through a quick internet search will not receive a great response; a little research will help you to move past general lack of information and pinpoint any more nuanced misunderstanding you might have, which is what this site is better suited to help with. $\endgroup$ – user122423 Jul 25 '17 at 23:24
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Who says that they don't? It's called spontaneous emission (sometimes also fluorescence or phosphorescence) and it is a key part of atomic physics. For more details, see any introductory textbook on quantum physics.

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