In case of Counterparty, burning Bitcoins is done as a means of distribution of the Counterparty tokens (XCP). Users receive an amount of XCP proportional to the amount of Bitcoin burned.

By burning the Bitcoin, instead of just collecting it as payment, the Counterparty developers have more incentives to make their own platform viable, unlike the various recent "ICO's", where the developers could retire on a tropical island with all the money they collected.
 Credit: https://www.reddit.com/r/Bitcoin/comments/6llq7p/eli5_why_do_people_burn_coins/