3 ideas
A position is what someone says they want; an interest is the underlying need, fear, or desire driving that demand. Reconciling interests rather than positions works because behind opposed positions there are usually multiple shared and compatible interests, and any given interest can be satisfied by several different positions.
Your Best Alternative To a Negotiated Agreement is the standard against which any proposed deal should be measured — the course you'll take if talks fail. Knowing your BATNA protects you from accepting unfavorable terms and from rejecting terms you should accept, and the better your BATNA, the greater your power in the negotiation.
When interests directly conflict, agreement should be based on standards independent of either side's will — market value, precedent, expert opinion, legal standards — rather than on a contest of stubbornness. Negotiating over which fair standard applies converts the clash into a joint search for legitimacy, so neither party has to back down to the other's pressure.