had no atmosphere is we would be bombarded with all kinds of incoming space debris.  This debris normally burns up when it enters the atmosphere, and rarely makes it all the way down to the Earth itself.  If you would like to see what the Earth would look like, take a look at the moon, with all its craters.  Those craters are the result of objects hitting the moons surface.  Another thing that would happen if the Earth had no atmosphere is the oceans would boil away, leaving no water here on Earth because there is not atmosphere to help complete the water cycle.  Admit it, you just got thirsty, didn't you?  And then, theres the problem of being the recipient of all the harmful radiation from the sun that the atmosphere normally takes care of.  The ozone layer would be nonexistent, so every time you wanted to go outside, you would have to either put on a radiation suit, or use a sunblock that has a solar protection factor of 3000!

Atmosphere does a number of things for us. For starters, atmosphere contains oxygen, the gas we need for cellular respiration. Without oxygen, we would all die very quickly. Atmosphere also protects us from the harmful ultraviolet (UV) radiations of Sun. It also prevents a large amount of space debris from reaching the surface of Earth. Extra-terrestrial objects burn up in our atmosphere and thus hardly ever reach the surface. Atmosphere is also responsible for greenhouse effect, which keeps the temperatures high enough for the life to survive and also ensures small variations between daytime and nighttime temperature. Atmosphere traps some of the solar radiations and keep the Earth warm, without the atmosphere, the surface temperature would be very low. Lack of atmosphere will also mean that all the oceans would evaporate very quickly (since water boils at lower temperature, when air pressure is low).

In essence, lack of atmosphere would have meant no life and no water on this planet, very low temperatures, high amount of solar radiations and bombardment by extraterrestrial objects. 

Hope this helps. 

The atmosphere serves several purposes for us here on Earth.  For starters, 21% of its composition is oxygen, which all animals must have to conduct cellular respiration, the process that helps cells manufacture energy.  1% of the atmosphere contains, among other gases, carbon dioxide, which is used by plants in the process of photosynthesis, the process which creates energy for all the plant cells.  The atmosphere also has a layer called the stratosphere, which has the ozone layer in it.  The ozone layer screens out harmful radiation from the sun.  If it were not there, we would have to wear radiation suits to go outside.  If Earth did not have an atmosphere, it would affect the water cycle, which is the redistribution of water across the Earth in a cyclical fashion.  Finally, the Earths surface would probably bear a closer resemblance to that of the moon, with all its craters.  The atmosphere causes most meteorites and other space debris to burn up before they strike the Earths surface.