A Coffin is used for keeping a corpse. It is also often referred to as a casket.
Information
For Humans
For humans, a coffin is mostly used to keep the deceased, either for burial purposes or for a cremation. For the cremation part, commonly, some chooses a wooden-type coffin for low-density fibreboard.
For Vampires
For vampires, a coffin is used some times as a bed - there, when dawn strikes; a vampire will arise from its coffin to haunt the villagers. However, these some times can easily backfire and a vampire hunter would take the chance to kill the vampire while they were sleeping, either with a wooden stake along with the help of a hammer, or a weapon blessed or made with silver. For reference, in the original 1931 Dracula film, Abraham Van Helsing killed Dracula while he was sleeping in his coffin with a wooden stake.
In Hellsing, these coffins were used for both, keeping the deceased and used as some kind of a bed for vampires. These coffins for vampires are some times specially made by their alliances, notably - the Hellsing Organisation, for instance; in the 2001 Hellsing anime, Seras Victoria used a special made coffin, in which, the lid of the coffin can go upwards or downwards with a control mechanism. However, in the original Hellsing manga, Seras used a normal coffin given by Walter C. Dornez.
Alucard's Coffin
A glowing white pentagram appears on Alucard's coffin.
Alucard's coffin is quite special, as it seems to be a mechanism to unlock level zero, as when he said the "Bird of Hermes" quote, Alucard's coffin, in which, was hidden in the SR-71 Blackbird, opened and Alucard was able to release his full power. Alucard had also mentioned about how his coffin is where he was born, and where he would die. Alucard himself, just like Seras, uses this coffin to sleep, however, he often uses a chair to do so, as he can be seen some times sleeping on his "throne". His coffin would later on can be seen in the basement where Alucard had previously met the Hellsing Organisation's leader, Sir Integra Fairbrook Wingates Hellsing.
It is noticeable that when Alucard releases level zero - in the center of the coffin, a what appears to be a pentagram or some sort appears with a glowing white color. Shortly before blood starts to appear and the coffin opens itself.
It is also shown in Hellsing: Dawn, Alucard's coffin can grow hands and uses them to run, attack, and etc.