How Does the Curvature of Space Affect Our Perception of Gravity?

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In many places (here in forums and on a few documentaries) when talking about relativity, it is often said to consider the space like a piece of cloth,fine net etc. If we think of it that way, shouldn't everything be on the same level in space? And then why do people on South Pole feel gravity towards the centre of the earth? Because space is being curved beneath them.Please forgive me if I'm missing something very basic.
 
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That's taking the analogy too far, in my opinion.
 
hamster143 said:
That's taking the analogy too far, in my opinion.

Will you please explain.
 

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