Right of first refusal is the right to make an offer before offers from others are considered.
For example:
Alice has a desirable widget. Both Bob and Chris would like to purchase Alice's widget. If Bob has the 'right of first refusal', Alice must hear Bob's offer before she makes any agreement with Chris.
Right of first refusal does not guarantee your offer will be accepted.
Also, a right of first refusal might imply a lower sales price for the seller (opportunity lost).
For example:
Alice hears Bob's offer, and then hears Chris's offer. Now, it is likely that Chris knows Bob's offer and can give a lower price than Bob's.
Alice hears Bob's offer, and then hears Chris's offer. Now, it is likely that Chris knows Bob's offer and therefore can get the widget for a just few cents above Bob's offer.