An espresso is a single shot of coffee produced by a coffee machine. In general coffee of this sort is used to make any of the common coffees you can order at any good coffee shop - so a long black, latte, "Americano", macchiato etc are all produced with an espresso base.
With instant coffee crystals, they will have some instructions on the side of the container that tell you how to make 1 cup of coffee - the volume of crystals to use for this is equivalent to the amount of coffee to deliver the flavour for a standard cup and hence is equivalent to the amount to produce 1 espresso.
Edited to add: It would take experimentation with any brand of instant coffee to get a decent conversion between it and espresso in flavour and strength because each brand is different in flavour profile and strength, though most use a "heaped teaspoon" per cup in my experience. However, FuzzyChef's answer is the right one here if you aim to get the espresso flavour coming through properly.