This is a topic which is confusing at first look and difficult as you begin to understand the intricacies.
To start with, the rule against perpetuities is part of a larger structure of future interests. Very briefly, a future interest is a second transfer of property from an initial transaction. For example, say you own a farm, but you want to get out of the agriculture business. Your child is not old enough to take over the family farm yet. So, you lease the farm to your neighbors, on the condition that in ten years full and complete ownership goes to your child. The present interest is the lease, the future interest is the full title to property.
Now lets change the situation a bit. Instead of at the lease ending and immediately going to the child, the transfer is conditioned. For example, the property is given to the neighbor so long as the property is used for farming, if the property is to change character than it is to go to the child. This is a conditional transfer to the child. The problem is this condition could never occur. The Neighbors could farm for ever, in that event the second transfer would never occur.
Think of it this way, the idea is to keep a complete title to property. When there is this hanging right for a transfer to a third party, the title is incomplete, which creates problems going forward. This is the problem the rule against perpetuities is designed to combat. The rule says that if there is a question of if a future interest would ever vest, then that secondary transfer is void.
The question then becomes of how to know if an interest would vest or not. There are two ways to look at it. The first, and simpler, is a wait and see approach. Many states have this for more recent transfers, giving the interest a hundred years to transfer over. If it does not transfer in that time frame, the future interest is removed. However, for older transfers the question of if the transfer will vest “not later than twenty-one years after the death of some life in being at the creation of the interest.” This is the part of the rule which is difficult.
A life in being is any person born or alive at the time the agreement was signed. This could be an individual who signed the agreement, such as the neighbor in our example. Or it could be someone specifically named for the purpose of being the life in being, such as a newborn or some unrelated individual. This gives the time frame. The question of vesting is a question of if the future interest will trigger in the given time frame. In the example we have, the condition of the property being used for a purpose other than farming may not occur ever or within the time period. Thus the rule would void the transfer over.
This is a complicated area of law, with each of the future interests deserving their own article. For the time being, keep in mind the rule against perpetuities may apply in complex transactions where a property goes to multiple holders.