If you're human it can be hard to see your limits. You can't stand outside yourself and be objective. The limits look to be part of the world, 'what's natural'. But, there are ways of exploring those limits, and learning about them can be quite useful in seeing how the human world works.
Why be concerned about limits, physical or intellectual? Because humans are tool users, and tools let you transcend 'built-in' limits. Most of human history has been about manipulating the physical environment to allow things that 'naked' humans couldn't do. Creating clothes, ways of getting or storing food or water, secure places to rest, raise children. More recently ways of manipulating information beyond what speech and writing make possible have been developed. These information manipulation tools ('computers') allow thinking about human intellectual limits.
This is not to say computers are 'thinking machines'. This is an easy mistake to make because the only previous ways of manipulating information was to use human thinking, so computers'll obviously be compared with that. Human thinking is about human survival, other humans, curiosity, maybe spirituality. Computers are about how information interacts, without any will, any sense of purpose, and while they have limits these are differently shaped to human ones.
Computers help us think about information, and how it is manipulated. The human mind doesn't seem to directly perceive the world, more filtered views of it, on the basis of memory, previous experience. Actions are then taken, more or less automatically, on the basis of what is perceived. If we look at this filtering as managing information we can start to see where the human limits might be.
Messing with information is a very human thing to do...
Information on Wikipedia
Claude Shannon on Wikipedia
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