Consensus is an ideal and the method of coordination between individuals in a decentralized system such as Bitcoin or other open source projects. Consensus is not a form of democracy: there are no forms of voting, representation, credentials, or gatekeeping involved in a consensus-based system. Nor does consensus require 100% agreement. Consensus is an ideal in the sense that, in most cases, there is no absolute agreement between all parties involved.
Consensus is required at multiple levels of Bitcoin: consensus must be achieved in maintaining the Bitcoin source code, and it must be maintained between all nodes storing and validating the blockchain. At the source code level, consensus is achieved by allowing anyone to propose, review, and comment on changes. This process is usually slower than centralized projects because discussion and review is applied intensively to any change before it is implemented. However, this process ensures that no special interests are served over others, and no private parties are capable of dictating Bitcoin’s future for their own gain.
At the blockchain level, consensus must be maintained by all nodes running compatible code. All nodes must agree on core parameters such as how many new bitcoin are created per block and what blocks and transactions are valid. Additionally, nodes must agree on the exact state of the network—which blocks comprise the blockchain and which transactions are included therein. If nodes disagree on these parameters, the network will fracture and the blockchain will splinter into several chains. Reconciliation between competing chains is extremely difficult, so maintaining consensus is of utmost importance.