ORCA: How to plot an adiabatic potential in dihydrogen H2 molecule?
By adiabatic, I presume you mean the Born-Oppenheimer approximation (which is usually used). If you need a plot of potential against H-H distance, then you need to do a relaxed potential energy surface (PES) scan.
! UHF OPT def2-QZVPP 
%geom Scan 
B 0 1 = 0.3, 1.3, 30
end
end

* xyz 0 1
   H       -4.61685        1.79381        0.00000
   H       -4.14986        1.26166        0.00000
*

The Scan directive in %geom section will perform a relaxed geometry scan (although in this case you have only two atoms so there is no difference between relaxed and unrelaxed). The B 0 1 = 0.3, 1.3, 30 line will scan the bond (B) between atom 0 and atom 1 (in Orca, atom counting starts from 0). The scanning will start from the bond distance 0.31Å and will end at 1.3Å and will go through 30 steps (i.e. the PES will have 30 points in total).
Another thing is that you need to use the unrestricted hartree-fock (UHF) because when the H atom splits the two electrons go into different orbitals, so RHF will give the wrong behaviour at higher bond distances (it will force double occupancy in one orbital, resulting in $\ce{H+}$ and $\ce{H-}$ fragments). UHF gives the right behaviour but may not reproduce the correct energy. Multi-configurational methods might be required.
The input file that I have shown will show you the energy behaviour of the ground state (in your graph, $\mathrm{U_S}$). Plotting the first excited state (antibonding) i.e. the $\mathrm{U_A}$ graph would be more difficult. You would probably need to do some sort of orbital rotation to converge to the excited triplet state, and then use that as the guess for the geometry scan (or maybe do TDDFT). I don't know much about that.
After running the calculation, the energy values at each bond length will be printed out at the end of the .out file, and also as a .dat file. You can import the .dat file into Excel or other programs to get the actual visual plot.
Edit: If I am not mistaken, the $\mathrm{U_A}$ graph indicates the first excited triplet state, so converging to that UHF solution is easier, all you have to do is to set the multiplicity to 3 (*xyz 0 3). Using UHF/def2-SVP, the scan looks like this—

As you can see, the two curves are crossing whereas they shouldn't really cross. I am not entirely sure why this happens, but I suspect that using multiconfigurational methods will solve this. Also note that the energy plotted is the absolute SCF energy, so the graph's don't go to zero at high bond distances.