In cryptography, a ring signature is a type of digital signature that can be performed by any member of a group of users that each have keys. Therefore, a message signed with a ring signature is endorsed by someone in a particular group of people. One of the security properties of a ring signature is that it should be computationally infeasible to determine whichof the group members' keys was used to produce the signature.
A ring signature makes use of your account keys and a number of public keys (also known as outputs) pulled from the blockchain using a triangular distribution method. Over the course of time, past outputs could be used multiple times to form possible signer participants. In a "ring" of possible signers, all ring members are equal and valid. There is no way an outside observer can tell which of the possible signers in a signature group belongs to your account. So, ring signatures ensure that transaction outputs are untraceable. Moreover, there are no fungibility issues with Monero given that every transaction output has plausible deniability (e.g. the network can not tell which outputs are spent or unspent).