|Bronze AE18 of Miletos in Ionia, c. 200 BCE|
These statues are well known now, as they were then, largely because copies were widespread. It is only these copies, and sometimes only descriptions, that have survived into the present. Copies were installed as decorative works in public buildings and even in the more luxurious private houses and gardens, particularly in Roman times; just as you can find some "classical" statues even now in garden centres. To have such famous and impressive works of art, even as copies, would have added prestige.
Several of these were also reproduced on ancient coins. For example, the poses known as Apollo Musagetes, Apollo Lykeios, Apollo Sauroktonos and Apollo Smintheos. I have a web page on Apollo on ancient coins which shows these among other Apollo images, and tells a bit more about them.
The coin shown here is quite scarce. It shows a cult statue of Apollo from a sanctuary in Didyma, and hence often known as Apollo Didymaios. Didyma (now Didim in Turkey) was in Ionia, close to the town of Miletos and within its territorial boundaries, and because it was a famous oracular centre it was honoured - and advertised - on Miletos' coins. The ability to foretell the future was one of Apollo's powers; the most renowned oracle in the ancient world, at Delphi, was at a temple of Apollo, and the centre at Didyma was almost as well known.
Apollo is holding a stag on his outstretched right hand, and has his bow in his left. The huge original statue was in bronze, and was created by a sculptor from Sikyon in Corinthia called Kanachos, in the late 6th century BCE. Kanachos is also known to have created another statue of Apollo in Thebes, this time of wood.
The history of the sanctuary at Didyma, its mythical origins and eventual destruction, is long and involved and I will not repeat it here. You can read some of it in this post by Jochen on the Forum Classical Numismatics Discussion Board. And for a detailed look at another Apollo type on ancient coins, here is Pat Lawrence's study of Apollo Sauroktonos on ancient coins.