In a double spending attack, the attacker sells say bitcoin for dollars. The bitcoin transfer is registered on the blockchain and then, perhaps after some escrow period, the dollars are received by the attacker. As soon as the bitcoin transfer is registered in a block–call this block 1–the attacker starts to mine his own blocks which do not include the bitcoin transfer. Suppose there is no escrow period then the best case for the attacker is that they mine two blocks 1′ and 2′ before the honest nodes mine block 2. In this case, the attacker’s chain–0,1′,2′–is the longest chain and so miners will add to this chain and not the 0,1… chain which becomes orphaned. The attacker’s chain does not include the bitcoin transfer so the attacker still has the bitcoins and they have the dollars! Also, remember, even though it is called a double-spend attack it’s actually an n-spend attack so the gains from attack could be very large. But what happens if the honest nodes mine a new block before the attacker mines 2′? Then the honest chain is 0,1,2 but the attacker still has block 1′ mined and after some time they will have 2′, then they have another chance. If the attacker can mine 3′ before the honest nodes mine block 3 then the new longest chain becomes 0,1′,2′,3′ and the honest nodes start mining on this chain rather than on 0,1,2. It can take time for the attacker to produce the longest chain but if the attacker has more computational power than the honest nodes, even just a little more, then with probability 1 the attacker will end up producing the longest chain.