Okay, so this is going to be long, so I apologize in advance and if I screw up anywhere, please feel free to point it out to me as I'm not totally an expert in this, I'm just applying what I know.
So the first thing to note is that the composition of an atmosphere is highly dependent on the life-forms that use it and vice-versa. (For us Humans, we need Oxygen, it's about the only element of our atmosphere that we actually use in day-to-day life)
Which means we really need to talk about the ecosystem in play. Plants use Photosynthesis, which converts Carbon Dioxide and water into Oxygen and Glucose(sugar) via the following method:
$6CO_2 + 6H_2O → (Sunlight-and-Chlorophyll) → C_6H_{12}O_6 + 6O_2$
Plants, along with other lifeforms also use respiration, which actually uses the reverse equation, which does not require Chlorophyll or Sunlight:
$C_6H_{12}O_6 + 6O_2 → 6CO_2 + 6H_2O$
Next, we need some way of creating lifeforms, this generally requires Nitrogen (For Amino Acids, proteins, and genetic material) and is why our own atmosphere has such a high percentage of it, despite not being needed for the above processes. Instead the Nitrogen Cycle is used as follows:
Method 1: Lightning Fixation (Note: No known amounts, Please fix if you know)
$N_2 + H_2O$ + $\mathrm{e^-}$ → $NH_3 + NO_3$
Method 2: Biological Fixation
$N_2 + 3H_2 → 2NH_3$
Now that we've got our Ammonia and Nitrates, we can continue through the Nitrogen Cycle to Nitrification as follows:
$2NH_3 + 3O_2 → 2NO_2 + 2H^+ + 2H_2O$
and then
$2NO_2^- + O_2 → 2NO_3^-$
Plants utilize the nitrate as a nutrient. Animals obtain nitrogen by eating plants or plant-eating animals.
When plants and animals die, bacteria convert nitrogen nutrients back into ammonium salts and ammonia. This conversion process is called ammonification, which then is followed by denitrification, which completes the cycle as shown below:
$NO_3^- + CH_2O + H^+ → ½N_2O + CO_2 + 1½ H_2O$
So, we've actually listed our main requirements for life on Earth already, even if unintentionally from these processes.
- Nitrogen ($N_2$)
- Oxygen ($O_2$)
- Water ($H_2O$)
- Carbon Dioxide ($CO_2$)
Now we know what makes up life as we know it, it's time to answer the second part of your question, concentrations, specifically how much concentration is needed for life, as we know it, to flourish.
It doesn't matter
Let me explain, as long as you've got some amount of all four of these elements mentioned above in your atmosphere you'll find that life can and does survive. Recreational Divers use Enriched Air Nitrox, which contains a higher percentage of Oxygen to regular air, 32% and 36% are common; and some technical divers use anywhere from 50% to 80% Oxygen as a decompression gas due to its lower partial pressure of inert gases (More info here)
However
Too high an Oxygen concentration will kill, as will too low an Oxygen concentration; which is why Pure Oxygen (100%) is strictly restricted and has limited uses (See here); and why going up mountains without air tanks is incredibly stupid and dangerous. (Over 7,000 feet (2,100 meters) is considered risky, as oxyhemoglobin saturation levels plummet and over 26,000 feet (8,000 meters) is considered the "death zone"; though anywhere over 11,500 feet (3,500 meters) is considered to be too dangerous for untrained humans to breathe in) - More info here
In Summation
I would recommend any potential, budding WorldBuilders to seriously consider what kind of world they are building and what kind of lifeforms they wish to inhabit its surface before trying to take atmosphere composition into account, as these figures and compositions are for Life here on Earth and may be different for other Life that we, Humans, are unaware of.
