Threshold signatures are digital signatures which require a subset of signers among the whole group to produce signatures on behalf of the group. The number of signers in the subset should reach a threshold, for example, a ( t,n )-threshold signature scheme is a digital signature scheme where any t or more signers of a group of n signers can produce signatures on behalf of the group. And a threshold signature does not reveal the actual group members that have cooperated to produce it.
The below links provides more details of principles of threshold signature scheme as well as comparisons with other algorithms.
The following links provides its usages and designs.