Seal clubbing is the common name for seal hunting, most specifically of the harp seal. Harp seals are sought after for their coats which are incredibly warm due to their 350,000 hairs per square inch. As a comparison, the average human has about 100,000 hairs on their entire head. For the first two weeks of their life, baby harp seals have a snow white coat to help them blend into the ice flows on which they live. This white fur was and is highly prized as a luxury clothing item and many baby seals were killed for their coat. The hunting of baby seals or so-called "whitecoats" has subsequently been banned in Canada since 1987 but it is still legal in other sealing nations (notably Russia) which still harvests the valuable white furs.
In most seal hunting nations, there are three legal weapons to hunt a seal with: a traditional Norweigian tool called a hakapik, a rifle or shotgun, and a club. Firearms are not preferred for hunting seals because of the danger, the difficulty of use, and the costs to the hunters. For obvious reasons seal pelts with bullet holes in them are worth far less than intact pelts. It's also much more difficult to kill a seal in one shot than it is to club them--imagine trying to shoot something accurately while standing on a rocking boat in the open ocean. What frequently ends up happening is that the seals are wounded and then dive into the ocean to escape, bleeding to death slowly. Ricochets off the ice also happen, presenting a danger to the hunters.
As a result, hunters club seals as often as possible. However, despite its name, most seal clubbing is done with a hakapik, not a club. The hakapik is roughly similar to the medieval war hammer and looks like a large claw hammer with a handle from 3.5 to 5 feet in length and a head with a blunt hammer face on one side and a pick or hook on the other. The hammer head (as well as the leverage from the long handle) is used to kill the seal without breaking the pelt, delivering a powerful blow to the seal's skull and (in theory) instantly killing it. The pick side is then used to drag the carcass to the boats following a hunt.
Currently the seal harvest is regulated by individual governments with quotas based on annual suggestions from the International Council for the Exploration of the Sea. Canada still hunts adult seals and, in fact, the Canadian seal hunt, which begins in late March or early April depending on the ice conditions, is by far the largest, taking in about 300,000 of the estimated 450,000 adult seals hunted annually. The remaining 150,000 are hunted by Greenland, Norway, Russia, and Namibia.