The world "relicensing" doesn't exist in copyright, nor in the linked article. Instead there are some similar situation being bunched together and faulty used interchangeably.
A copyright author can redistribute a work they own under new terms. This would be the case when they have offered a work under say MIT and change the copyright license for any future offer under the GPL. It is similar to a merchant changing the price, ie in the past the product cost X but now it cost Y. Naturally past customers don't suddenly have to pay more for something they already paid for, but buying more (or getting updates) applies the new price.
The copyright author can also dual license it. In this case they would offer the work but under two different licenses at the same time. This would be like a merchant offering a product under two payment plans, one where you pay up front and an other more expensive method where you pay a small amount each month for a bigger total. In both cases the product is the same but the condition of sale is different.
The MIT license itself also allows for something similar to resellers, ie people who take a copy and apply their own additional set of conditions when they distribute it. This doesn't change the original offer, but those getting a copy from the reseller has to honor the resellers term and condition in addition to the original conditions of the author. This is similar to going to a store where you pay both the product original price and the margin of the reseller. You can always go to the original manufacturer and only pay the original price, but you may miss out on features that the reseller include in their package.