Most states have sales tax (five don't: Alaska, Oregon, Montana, New Hampshire, Delaware). Their sales tax applies to ANY purchase their citizens make, regardless of the place of sale. It's a little more complicated sometimes, for instance if you bought it out of state, they may charge a "use" tax, since the sale wasn't in their jurisdiction, but in general it's the same essential thing - you must pay a tax if you spend money on something. Generally post-sale taxes are collected at the same time as income tax returns.
The states hand out business agreements with businesses and that agreement requires the business to collect sales or use tax at the time of sale. Thus the state can force business within the state to collect the relevant sales tax at the time of sale.
However, the state cannot force a business outside the state to collect sales tax. So for many, many years, mail order companies reaped the benefits of being able to sell expensive items to customers who wanted to dodge sales tax. If the shipping cost was lower than the tax, it was win-win for the customer and company, but the state lost on sales tax the customer should have declared at tax time.
States, for many years, didn't feel it was a big enough source of income to try to go after (although some did attempt to do it).
However, online commerce is turning into a big piece of the pie.
The states can audit people and if they didn't declare their sales and use taxes properly (yes, you generally have to pay sales tax on item you bought from a friend - it doesn't have to be a business).
But more and more states are entering into reciprocity agreements with each other. For instance, Ohio requires businesses that sell to Michigan residents to collect Michigan sales tax and send it to Michigan, and Michigan requires Michigan businesses to do the same for Ohio residents.
Ohio can't make Michigan businesses collect sales tax, but Michigan can, and therefore this reciprocity agreement forces businesses in both states to comply with tax laws in another state. These reciprocity agreements are getting larger and larger and gaining steam - I think Michigan has such agreements with 5 or so nearby states.
Some internet retailers are being pro-active about it and simply charging sales tax for everyone, such as Dell. Others use it as a competitive advantage and try to give items to their customers with the "tax" discount, even though their customers are still liable for it.
What Amazon and others are trying to do is set up shell corporations to manage their warehouses. So, if Amazon sells to me in Michigan from the "Amazing Fulfillment Warehouse Company Number 43", which technically is a separate company from Amazon, and he warehouse is located in Michigan, does Amazon - which has not signed a business license with Michigan, owe sales taxes? The fulfillment warehouse is a service provider to Amazon - they didn't sell anything to me. Amazon pays them for storage, order fulfillment, and shipping, so technically the business license they signed with Michigan doesn't mean anything regarding collecting sales taxes for me.
So, legally, Amazon and many other businesses are attempting to get out of paying state sales taxes through various tricks. Technically it should be OK, since, in theory, I should be paying sales taxes to Michigan for things I buy that don't automatically charge me tax. But I don't - I'm not going to bother keeping track of all my purchases and fill out paperwork so I can send money to my state, even though I could be fined for it. It's not worth it. And most people do the same thing.
So the states craft labyrinthine tax codes and business agreements in order to make it so Amazon and other major retailers pay sales tax, so they don't have to work so hard to get it out of their citizens.
And Amazon is fighting back so they can have a competitive advantage over local businesses who do have to pay sales tax.
So, do I go to Locally Owned Joe's Diamond Emporium and put money back into the local economy, but spend an additional $30 in taxes, or do I get something from Amazon with free shipping and no taxes, but my money goes out of state?
Local businesses are at a severe disadvantage. Moreso because their customer base is smaller, their inventory is smaller, their orders to suppliers are smaller, and shipping to their location is more expensive, etc, etc, etc. They can't compete.
So is it fair or right for Amazon and others? Well, they aren't operating illegally. But it's hardly fair.