Wine is made as an art form. You have to have the basic raw ingredients of high quality but given the same ingredients, you can get drastically different wines made. How long a red wine is allowed to sit on the skins (which allows its color to develop and tannins to leach into the mix) whether or not it’s aged in new oak, used oak, American Oak, French Oak; how long it was aged in the oak barrels, how long it was allowed to age in the bottle before release and a myriad of other factors all combine to give a wine its structure.
In short, it is the sum total of everything that makes the wine what it is. A wine may have adequate acid for example, but lacks the tannins to allow it to age gracefully and with some longevity. A white wine is sometimes (frequently) too sweet without an adequate balance of acid to counter the sweetness in which case the wine will just be sweet--disgustingly so.
So although a bit simplistic, a wine’s structure is the sum total of everything combined that makes the wine what it is. When it all comes together in the right proportions, like a quartet with the individual parts perfectly balanced, one listening would never be able to really pick out the individual harmonies. They create one gorgeous sound. When a wine is well made–well structured–the individual parts are balanced creating one, unified impression that is wonderful; that is what makes a wine well structured.