What does it mean to say consumers BID UP THE PRICE of goods when there is a shortage, resulting in an increase in the equilibrium price?

When economists talk about markets, they treat them as if every market is an auction.

Think about it this in terms of eBay.  If there's something up for auction there but there are a million of them, there's no shortage of it and people don't compete against each other to buy it -- there are plenty for everyone.  But then compare it with something rare -- the bids go up and up because there is, in essence, a shortage.

Another way to think about it is in terms of great NBA or NFL players.  There's always a shortage of those so the teams will pay them huge amounts when they become free agents.

It doesn't work exactly like that in the market for regular stuff, but it's the same idea.  When firms see that their product sells out all the time, they'll raise the price.  The consumers aren't literally bidding the price up, but the effect is the same.