In string theory, why does a higher dimentional moving object (a string) represent a particle?

Answer 1

String theory believes that different types of particles are really just strings that vibrate differently. The vibration of the string determines the properties of the particle.

String theorists found, in trying to describe the panoply of particles which we know to exist, that a string vibrating in three (Or four) dimensions does not provide enough permutations to describe them all.

The thought is that the only way you can have complex enough string vibrations to describe the whole catalog of particles is for some of the vibrations to take place in other, as yet undiscovered, dimensions.

Read Brian Greene's "Fabric of the Cosmos"

Later edit: I like Piglet O's answer too.

Answer 2

it is an oversimplification but imagine a plane with a line going through it. if you are a resident of the plane, where the the line is in the plane is only a point.
similarly, a multidimensional string as it passes through our dimension, is only in our dimension enough to appear as a particle.