What is the general idea of a sybil attack?
A Sybil attack is made possible by some entity (or group of entities) creating many-to-one identities on a network in order to gain outsized influence.
This is often possible where there is low or no barrier to entry into a network.
In the case where a network provides participants with anonymity, a participant is easily able to anonymously pretend to be many act as many different people.
The benefits of having multiple identities on a network could be wide-ranging - however a popular example is that of some democratic vote.
If a decision occurs based on number of votes, someone can artificially inflate the number of votes to influence the decision in their favour.
This would be a garden variety Sybil Attack.
What deficiencies within a system (such as a cryptocurrency network) can allow a sybil attack to occur?
Where participants of a system are anonymous or pseudo-anonymous, entities can join the network with low barrier-to-entry.
When there is low, or no barrier to entry, the can easily derive multiple private keys and have multiple identities.
As far as the network is concerned, the individual who holds 100 different private keys are 100 different people.
If there were to be some vote which takes into account the number of private key signatures voting on some option, a person could create many identities to influence the decision to their favour.