The fat guy is the Emperor Nero, and the coin is a silver denarius. It is small, about the size of a U.S. dime, but it was an ordinary daily wage for a worker. (For a lot of information about Roman money, see Everett Ferguson, Backgrounds of Early Christianity (2nd ed.) p. 85.)
What does that mean today? If a U.S. worker is paid $20 per hour and works an 8 hour day, a denarius is $160.
The denarius is quite important in the N.T. Gospels. In John 6:7, we are told that it would take at least 200 denarii to feed 5,000 people. Do the math, and it comes to about $6.50 in today's U.S. dollars. This is quite close to the cost of a basic meal in a fast-food restaurant.
The idea that a daily wage today is about equivalent to a daily wage in the Roman Empire works out pretty well.
Another sum of money that shows up in the New Testament is the Talent. This is about 6,000 denarii, and it weighs about 80 pounds avoirdupois. In today's money, one talent would be almost one million USD. (A talent would pay an ordinary worker's expenses for about 20 years, and that is also true of one million USD.)
When Jesus told the "Parable of the Talents" (Matt. 25:14-30), he was intending to astound his audience with the amount of money involved. In the parallel story, Luke 19:12-23, the amount (a Roman mina) would be about $16,000, still a significant sum.
This coin is in the British Museum, CM1860-3-30-44/BMC Nero 91. Photo by Richard Davies, with the usual restrictions.