To understand the aphorism, one must know the idiomatic phrase "to beat a path".
When many people walk on the same path (through a patch of grass, for example), eventually the grass gets worn down. After time, even the soil underfoot becomes hard and smooth. When this happens, we say that the path has become "beaten".
(Note that the phrase "off the beaten path" uses the same basic idea.)
So in the aphorism "Build a better mousetrap, and the world will beat a path to your door", the literal meaning is that if you build a mousetrap that is far better than any that have been previously invented, the people of the world will come to your door in such great numbers and frequency that the path to your door will become beaten.
Because it is an aphorism, it does, of course, have a figurative meaning. The idea expressed here is that a useful innovation will draw many customers. Your reading is correct.
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