It might be easiest to explain MMT by contrasting how the budget of the United States differs from a household budget:

1. If your household wants more dollars, you have to do work, invest, get a loan, etc. If the United States wants more dollars, it can (and does -- this is actually how significant government spending happens) literally just print them.
2. Because you might not be able to obtain enough dollars to cover your debts, you can default on a loan or not have enough money to pay your bills. Because the United States can just print more dollars as needed, it can never default on its loans and will always be able to pay its bills (at least as long as both of those can be paid in U.S. dollars).
3. At some point you want to pay down your debts to zero. The United States doesn't want to do this, because U.S. debt creates the Treasury bill market, and paying the debt down to zero would eliminate that market.

There are limits to this -- if the United States prints too much money, and/or doesn't recover enough in taxes, inflation will rise and create all sorts of economic problems -- but we're currently doing historic deficit spending and have consistently low inflation, so we're likely not close to those limits.

As for why this is bad from a leftist perspective: it's not.