I can't talk about the welfare optimising effects but it's a more efficient way to generate a similar outcome to a classic 'bid upwards' English auction - I assume you know the process of that.

Imagine we have four people competing, who each have a max bid of:

Alice: 100, Bob: 150, Charlie: 155, Diana: 180,

In a standard auction bidding would, say, start at 50. When the cost exceeded 100 Alice would drop out, similarly for Bob at 150, and Charlie at 155. So Diana would win and pay 155 (plus maybe one bid-increment, depending on who bid first).

So, if each simply submitted their max bid under the Vikrey auction rules, Diana would win, and pay 155. The whole bidding upwards process can be avoided, which is by some standard more efficient, and everyone pays essentially the same as they would under and English auction.

In sealed auctions, you want to win by bidding the most. But if you win by more than $1, you could have paid less.

In this version, you just bid to win and the seller lets you adjust down to that perfect "just barely winning" bid afterwards.

It turns out the seller makes more by everyone bidding to win than they lose by letting the winner adjust their bid after winning.

That's because the 2nd place bid ends up being higher than the winner's used to be.

The winner pays the price that the 2nd highest bid.

This means all bidders in the auction have a reason to send an honest bid rather than trying to game the system.

The person "selling" in the auction also has an efficient outcome.

In a normal auction you take the highest offer, but stiff competition will cause the final offer to be too high. If we're talking about megarich people buying Rembrandts, who cares. But generally this is a bad thing: we're failing to discover the real value of the thing being auctioned, and we're being wasteful.

For bidding on jobs (e.g., highway construction) one normally takes the lowest bid, but the lowest bidder will not make any profit and might lose money on the deal, thus putting the project at risk. What might happen in those cases is that corruption takes root and the lowest bidder gets paid more money illegally.

In any case, sealed bid, second price bidding solves the problem by removing the incentive to offer the best price and instead offer the real value.