It is similar to Diffusion Monte Carlo, except that it works with paths rather than points.
This has some advantages relating to calculating certain properties of the system under study that diffusion Monte Carlo has difficulty with.
In both diffusion Monte Carlo and reptation Monte Carlo, the method first aims to solve the time-dependent Schrödinger equation in the imaginary time direction.
When you propagate the Schrödinger equation in time, you get the dynamics of the system under study.
Diffusion equations can be solved by imagining a huge population of particles (sometimes called "walkers"), each diffusing in a way that solves the original equation.
The update step in diffusion Monte Carlo would be moving the walkers slightly, and then duplicating and removing some of them.
"Reptation Quantum Monte Carlo: A Method for Unbiased Ground-State Averages and Imaginary-Time Correlations".
"Reptation quantum Monte Carlo algorithm for lattice Hamiltonians with a directed-update scheme".