Temperature is the main one. There are very few plants on the poles and few above certain altitudes (depending on latitude) due to cold temperatures. Rainfall as well. Desert plants are created to tolerate drought conditions and Tundra plants can survive in places where the water is locked up in ice.
I am agree with Andrew. He answered you from opposite side. I mean, he example places where there is no plants, such as poles, deserts, ..., and then explained the climatic parameter. I am totally agree with him about temperature and precipitation.
Agree with Andrew. beside temperature and rainfall some other factors are also responsible such as geographical position, anthroprogenic activities, climatic factors, river systems available, geography, geomorhology etc all have their own unique influence in vegetation cover and type of vegetation.
Some of the major climatic factors play important role in vegetation distribution as follows. In any eco-system, a living organism/vegetation is is influenced by a number of factors and forces. These environmental factors are known as eco- factors or ecological factors which include light, temperature, soil, water etc. These factors may be biotic (living) and abiotic (nonliving). The sum total of all these factors constitutes the environment of an organism.
All these ecological factors can be broadly classified into the following divisions:
(i) Climatic or Aerial factors:
(a) Light;
(b) Temperature;
(c) Water
(d) Rainfall,
(e) Humidity,
(f) Atmospheric gases (wind).
All the vegetation distribution is also affected by climatic Limiting Factors. There is a variation of tolerance from species to species with respect to a particular factor. An organism may have narrow range of tolerance for one factor but wide range of tolerance for other factor.as living organism and vegetation is linked with each other in complex manner with different cycles thus limiting factor should must be taken in account.
The main controls for vegitaton distribution are biological factors and environmental factors, as said by
Kundan. The biological factors are more difficult to understand and quanitfy, but consist of symbiotic relationships, geochemistry, and biologic interactions.
Manuals of biogeography give often the most important factors explaining the vegetation distribution and the main vegetation species on the earth surface.
Hein underlines most of the important factors.
Locally, you have also to take account of the nature and the thickness of soil, the nature of the bedrock, and also some topographic parameters (elevation, degree of slope, slope orientation, et.)
The annual mean temperature and the average number of days without frost during a full year are also factors about the distribution of vegetation around the world