The Dioscuri were more than dead mortal heroes back in the day; the twins were seriously popular gods and were worshipped all over the place. Their hometown of Sparta was particularly in love with them, but they were given props all over Greece and eventually became mad popular in the Roman Empire. Like all gods, Castor and Pollux became symbolic of the things they were thought to be patrons of.
Since they were said to be expert horsemen, they became symbolic of all horsemen, and were prayed to for help in all horse related issues. (Which we're guessing there were a lot of back then.) Because Pollux, especially, was known to be such a great boxer, they were the patrons of all boxers. With their horse skills and boxing skills together, they were prayed to by all athletes in general. You can bet that at any Olympic games or any gymnasium for that matter, there were a whole lot of prayers going up to the Dioscuri.
The twins were also the patrons of travelers and sailors. For sailors, they were especially important because they were said to cause the phenomenon we call St. Elmo's Fire today. It's when things that are high up gain static electricity before a thunderstorm and start to glow. Back in the day, though, sailors thought this was a sign from the Dioscuri that the ship would weather the storm.
Castor and Pollux were also patrons of warriors. Soldiers would pray to them in times of war and ask for their favor before a battle. Some say that Spartans used to carry into battle two upright posts joined by a crossbar to represent the Dioscuri. In the Roman Battle of Lake Regillus, the twins were actually said to have appeared and fought at the head of the army, winning the day for the Romans. In honor of them, the Temple of Castor and Pollux was built in the heart of city.