The first reason why Veteran Explorer is the best commander in PDH is because the deck is only running 27 lands. No, I'm not exaggerating, there are exactly 27 lands. This gives us an incredible number of available card slots, which means each card we draw is much more likely to be valuable to our gameplan when compared to our opponent's draws.
VE is a reliable source of repeatable land ramp for only one green mana, sitting right in the command zone. This comes at two costs: firstly, we also ramp our opponent's lands, and secondly VE needs to actually DIE (read, go to the graveyard) in order for his ability to trigger. This means we need to run a few cards which put him back into our hand from the graveyard.
A keepable hand for this deck only needs to include one land or Lotus Petal. From there you can cast VE and he will get the deck moving along smoothly without relying on drawing additional land cards. The deck also runs Land Grant to minimize the frequency of mulligans.
Of course, in order for the deck to do anything, VE needs to die. There are a few reasons and ways that this might happen: maybe our opponents are still naive to the sheer power of VE and haven't yet learned their lesson, or maybe a greedy player wants the mana ramp and (wrongly) feels as though they can outrace our value engine, or maybe our opponents are smart enough to leave VE alone for a while. The latter is the worst case scenario, as ideally we want VE to die before untapping on T2. If VE is still alive on T2, the correct play is to either swing into unfavourable blocks tempting an opponent to kill it, or if that doesn't work you can use one of the many "fight" effects in the deck like Prey Upon, Savage Swipe, Pounce, Unnatural Aggression or Epic Confrontation to have VE kill himself.
It will absolutely happen during some games where VE will just be stuck on the battlefield for the first 2-3 turns because our opponents wisely are keeping him alive. If this happens, you will almost certainly miss a land drop during this time, but don't panic! The deck is completely loaded to the brim with ramp effects and mana dorks to compensate for not being able to draw land cards consistently. Even if you fall behind by a land or two, as soon as the engine does get rolling and VE dies at least one time, the deck will catch up and quickly overtake our opponents in terms of resources.
