The right of first refusal is the right to be the primary buyer of an item. A party who has the right of first refusal does not necessarily have to buy the item. The right of first refusal simply means that they are the first ones who get to decide whether or not they would like to purchase it.
An example of a right of first refusal would be a situation where there are two partners in a business, and one of them is selling his or her share of the company. In this case, there may be a stipulation in the contract, which states that the other partner has the right of first refusal to the shares that are being sold. In other words, in these circumstances, the other partner would get to decide if they would like to buy the remaining shares before they are offered to other buyers.