Mars has a lot of carbon dioxide in its atmosphere. It also gets a lot of sunlight. On Earth, plants use carbon dioxide and sunlight for photosynthesis. So, why can't plants live on Mars?
Plants don't just need carbon dioxide; like most organisms, they need oxygen to survive as well. They can produce oxygen from carbon dioxide, but that doesn't help cells that aren't exposed to sunlight; if you put a plant in a very low-oxygen environment, it will die.
There are organisms that can survive on little to no oxygen (e.g. cyanobacteria, which can directly supply their respiration cycle from their photosynthesis cycle), but as a rule plants aren't among them.
All life as we know it requires liquid water as a medium (a polar solvent) in which the chemistry of life can take place. Mars surface conditions pretty much preclude the existence of liquid water. The atmospheric pressure is at or below the triple point of water, meaning that water can only exist as ice or gas (vapor). Even though Martian soil probably contains all the elements necessary for plant growth, and it appears as though Mars once had liquid water on its surface (it would have had a thicker atmosphere back then), plants could not survive in current Martian conditions due to the absence of liquid water.
If the Martian atmosphere were a bit thicker, it could be a different situation, but, as pointed out in one of the other answers, plants actually need oxygen as well as carbon dioxide. In the presence of sunlight, plants consume carbon dioxide and produce oxygen as a "waste product". In darkness, plants still have to support their metabolism and consume oxygen from the atmosphere to do so. Apart from that, plants are not islands of life; they have symbiotic relationships with other organisms including bacteria. Some of those organisms require oxygen too.
Life may once have existed on Mars, which is largely why so much exploration of it is being done now. There is evidence of flowing water, which implies a warmer climate and thicker atmosphere. But that atmosphere was stripped away as the sun grew hotter, and now Mars is frozen. It doesn't have enough gravity or a magnetic field strong enough to hold in an atmosphere thick enough to keep it warm, with the sun the way it is now.
Plants need liquid water. Mars today has none. Well, actually it does, in the summer, for a few hours each day. Because of the presence of perchlorates in the soil, the melting temperature of water is lower, it works like antifreeze. This is enough to allow it to exist briefly in a liquid state. But then it freezes again. That brings up the matter of the extreme swings in temperature between day and night, because there isn't enough atmosphere to even temperatures out. At the equator, temperatures vary by about 100oC each day and in mid-latitudes by about 60oC. Aside from water issues, such big temperature swings present a challenge to any life form, though some can handle it.
As said by cpast, plants also make use of oxygen and will die without it. They only need a little. It is used to process nutrients drawn from the soil. On Earth, the evolution of plants began after cyanobactria began to produce oxygen as a metabolic byproduct, which eventually caused atmospheric oxygen to build up. Cyanobacteria seem able to survive on Mars, so if there weren't other problems, this mechanism could also have occurred there. Alas, the other problems already mentioned made that impossible.
Things lacking for Mars to grow plants:
Water. Think that's well covered.
Atmosphere. Even if it had a similar composition to earth's, it's simply too thin. Lack/Loss of magnetic field led to Mars's atmosphere being mostly stripped. If you were to give it a full 1 atm pressure today, this too would disappear. So if you plopped an earth plant on Mars, it would be voided of most of it's gases and die.
Loss of Magnetic Field. Except for small pockets, Mars's magnetic field is too small to protect the surface. This means far more radiation gets to the surface. If the above didn't kill plant life, the radiation level would. The plants cancer would get cancer.