There are different ways to do parallel programming with Julia.
If your problem is very simply, then it might sufficient to use parallel for loops and shared arrays:
https://docs.julialang.org/en/v1/manual/parallel-computing/
Note however, you cannot use multiple computing nodes (such as a cluster) in this case.
To me, the other native constructs in Julia are difficult to work with for more complex programs and in my case, I needed to restructure (significantly) my serial code to use them.
The advantage of MPI is that you will find a lot of documentation of doing MPI-style (single-program, multiple-data) programming in general (but not necessarily documentation specific to julia). You might find the MPI style also more obvious.
On a large cluster it is also possible that you will find optimized MPI libraries.
A good starting points are the examples distributed with MPI.jl:
https://github.com/JuliaParallel/MPI.jl/tree/master/examples