DomainA sphere of knowledge (ontology), influence or activity. The subject that the user is working a program on the domain of is software. The domain in DDD is the problem space. The corresponding solution space is called the model.
ModelA system of abstractions that describe selected aspects of a domain and can be used to solve the problems associated with that domain.
With DDD, we are looking to create models of the domain. Things which often places great effect at the beginning of a project, such as persistence, user interface and protocol. Model does not mean a graph or set of graphs e.g. UML. Charts are useful, but they are not the model, just different views of the model. The model is one that we choose to implement in software, represented in the code used to construct the system. The code itself is the model.
This gives certain expectations of the code. It shall be easy to understand and read. If the domain experts can understand a snippet of code describing their domain, the room for error shrinks. The standards set by Robert C. Martin in Clean Code is one way to accomplish this.
Ubiquitous LanguageA language built around the domain model and is used by all team members to connect all activities the team with the software.
This does not exclude the use of diagrams, symbols and text analysis. These are important tools for finding the model, and describe it before it gets into the code. Texts and informal sketches is a good starting point. We do not need any special design model or specific sets of symbols. This is because we are starting from the domain, the reality, and have to describe it in a way that is shared by developers and those who order the application, the domain experts. It is therefore extremely important to have a common description of reality and a ubiquitous language. This work is the basis for the whole architecture.