Dogecoin is a type of cryptocurrency. It has a notoriously volatile market history, with massive increases and decreases in value. This volatility makes it something of a "trader's dream", assuming the trader can play the market right with it.
Unlike many other currencies, Dogecoin allows for an infinite amount of coins to be mined. This was decided as an attempt to theoretically curb inflation.
Dogecoin takes its name from "Doge", an image macro format in which pictures of a shiba inu are overlaid with a variety of colorful, short phrases.
To an extent, the phrases are meant to represent the internal monologue of the dog; in media of this type, dogs are usually portrayed as frantic, impulsive and high-energy. There is no larger purpose of the meme other than goofy comedy.
Dogecoin is considered something of a "Producers currency". The play The Producers features an attempt by the protagonists to create a hilariously bad show that will fail spectacularly, but it instead becomes a hit. In a similar sense, Dogecoin was meant as a joke, but actually took off as a legitimate form of cryptocurrency.
Joe is a huge fan of Dogecoin, often attempting to shoehorn discussion of it into episodes of the show. Lars tries to avoid getting into the topic, as he does not engage in cryptocurrency trading and has no interest in discussing it.
On an episode with Misha Yurchenko, a cryptocurrency trading expert, Joe finally got his wish to discuss the coin at length. Lars had the guest on in order to indulge the latter.