As others have said, there will be extra fees to pay with most airlines unless you live like a monk.
For the most part (though there are exceptions) you should expect these fares to include no checked luggage, no food or drink, no seat choice etc. Hand luggage may be just a *very* small 'personal item' or might include something larger, depending on the airline, but you in any case will probably be smaller than you're used to in the US. If you let us know which airlines, we can give a bit more specific advice.
But yes, it can be very cheap to travel around Europe. Not always as cheap as the headline prices make it seem, but still incredible value.