The Crown is a term which is used to separate the government authority and property of the state in a kingdom, as opposed to any personal influence and private assets held by the current Monarch.
In the United Kingdom 'The Crown' represents all rulership in the Kingdom, but is separate from the person currently wearing it. For example, the Queen owns some of her castles herself, and if she abdicated, she would keep them. Others belong to the Crown, and would belong to the next monarch.
The Crown is therefore a 'corporation sole' i.e. a legal being which can own property and have rights. Elizabeth Windsor is currently the post holder, and thus Queen of the United Kingdom. The holder of the position of the Crown will be King or Queen and officially governs the UK. In practice, of course, the UK is governed by the government derived from the democratically elected parliament, but this is only done 'on behalf of the Crown' and many people in the country are 'Crown Servants'. For instance, traditionally, prison warders were directly employed by the Crown, and not by the Prison Service. The Crown is also the source of all justice (hence why we have the 'Crown Prosecution Service' in the criminal courts whose lawyers are called 'Crown Prosecutors'), which also meant that it was immune from prosecution. Thus all Government departments were essentially immune from prosecution, which was so unfair that it was limited slightly by the Crown Proceedings Act 1947. Crown servants may not sit as Members of Parliament and this is used as a way of allowing MPs to retire before their time - they are awarded a job which is that of a Crown Servant (the most common is 'Steward of the Chiltern Hundreds') and thus disbarred as an MP.
The concept of the Crown took form under the Feudal System, evolving from and synthesising oriental and barbarian concepts of kingship. Under the Feudal System, in England and (separately) Scotland, all rights and privileges were ultimately granted by the ruler (though this was not the case in all countries that had this system). All land was granted by the Crown to lesser lords, in exchange for feudal services, and they granted the land to lesser lords. One exception to this was common socage - owners of land held as 'socage' held it subject only to the Crown. The Crown as ultimate owner of all property also owns any property which has become Bona Vacantia including finds of treasure declared Treasure Trove.