While all the answers above are true and epimerization is the main argument in favour of using HOBt, it is also a nucleophilic catalyst, which means that it accelerates the reaction. The reaction will proceed with HBTU, but more slowly.
The reaction proceeds without HOBt, but as mentioned by above, it does help minimizing racemization thus is used as an additive. You don't need to add a lot and 2 equivalent is more than enough if you are using, but even if you use HBTU itself, the reaction goes perfectly fine, due to the byproduct of the coupling is HOBt.
Not really necessary but to avoid Racemization which is one of the main side reactions, when activating carboxyl groups of amino acids. Electron-withdrawing groups bound to the α-amino moiety will increase the tendency to racemiz considerably.
HOBt is one of the most effective suppressors of racemization in carbodiimide-mediated reactions. But is should be used carefully due to it's explosive nature in water free form.