What was Hobbes opinion of the nature of man? Why do they compete?  

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According to Thomas Hobbes, human nature is fundamentally competitive because everybody desires to accumulate possessions in the form of property.  Hobbes begins this chain of reasoning in his introduction to Leviathan when he argues that,

Nature (the art whereby God hath made and governes the world) is by the art of man, as in many other things, so in this also imitated, that it can make an Artificial Animal. For seeing life is but a motion of Limbs, the begining whereof is in some principall part within; why may we not say, that all Automata (Engines that move themselves by springs and wheeles as doth a watch) have an artificiall life? For what is the Heart, but a Spring; and the Nerves, but so many Strings; and the Joynts, but so many Wheeles, giving motion to the whole Body, such as was intended by the Artificer?

This portrait of the human reduces all human life to mere "motion of the Limbs."  By comparing the "Heart" to a "Spring," and "Joynts" to "Wheeles," Hobbes implies that people are just a collection of matter in motion.  The remainder of Part I goes on to describe man in more detail, eventually demonstrating that this materialist account of the human leads to a desire, on the part of every person to increase his or her power over others because of their natural penchant for vainglory.

In Chapter X, Hobbes argues that men work to increase their power by their nature:

The POWER of a Man, (to take it Universally,) is his present means, to obtain some future apparent Good. And is either Originall, or Instrumentall.

Because man's appetite naturally inclines them to seek the "Good," all men wish to increase their power.  Importantly, all of Hobbes' examples of power imply some kind of power over others.  For example, he claims that, 

Riches joyned with liberality, is Power; because it procureth friends, and servants: Without liberality, not so; because in this case they defend not; but expose men to Envy, as a Prey.

Thus, riches serve to empower the person who possesses them by allowing them "friends, and servants."  Conversely, it not "joyned with liberality," riches decrease a man's power because it "expose[s]" them to others who "Envy" them.  This calculus of power and desire embodies Hobbes' fundamental thesis on the nature of man.