You might be familiar with decisions made by consensus: Everyone has a veto right. Decisions made by consent are slightly different in that vetos need to be reasoned objections, i.e. they need to demonstrate how the proposal would lead to unintended consequences, based on goals that have been defined before. (Called drivers in S3, or the circle’s aim in Sociocratic Circle Method.)
Note that in reality, groups doing decisions by consensus often only use their veto powers when they have reasoned objections – some are even offended by sociocracy people defining a new term and contrasting it with consensus as if there was anything wrong with it.
The term “consent decisions” is used mostly by sociocracy people, hence it also carries the connotation that decisions would not be made by the entire group, but rather circles to which the responsibility for certain domains are delegated. In effect, the idea is that decisions are made neither by “the king”, nor “the majority”, nor “everyone” (having veto rights), but by “the best argument available to the group who has been appointed to make the decision”.
For more reading, see the PDF Consent decision-making by sociocracy for all – especially the introduction (section 1), which explains consent. The other sections deal with the consent decision process as used in meetings, which might also help with understanding consent itself.
(Sorry for linking to entire websites over at Reviewing the process for consent decisions…)