A coordinate representation of density matrix $\rho$ is defined as
$$ \rho (x, x') \equiv \left<x\right| \rho \left|x'\right> .$$
When $x = x'$, this expresses a probability where a particle is in the state $\left|x\right>$.
Question: what does that mean when $x \neq x'$? Is that related to some probability?
According to Feynman (Statistical Mechanics a set of lectures, (p.72)),
$$ I \equiv \int dx _1 \int dx _2 \cdots \int dx _{n - 1} \left<x\right| \rho \left|x_1\right> \left<x_1\right| \rho \left|x_2\right> \cdots \left<x_{n-1}\right| \rho \left|x'\right>$$
can be interpreted as that "the particle travels from $x'$ to $x$ through a series of intermediate steps, $x_1, x_2, \cdots, x_{n-1}$, which define a path". I don't understand this statement.