The implementation phase of the waterfall should be the most familiar to you, as it is the actual process of creating the proposed software system. This is, after all, the subject of most of your early coursework - the basics of programming, algorithm design, and considering time and memory complexity of your employed algorithms.
It is critical that the implementation adhere to the details provided by the design, as this ensures that a large body of programmers can work independently on the aspects of the system. But despite the best efforts of the designers, it is not uncommon for some critical details to be overlooked. In a properly implemented waterfall process, this kind of “splashback” is anticipated, and a process exists for proposing, approving, and disseminating changes to the design. Because these changes can cause problems for the other programmers working in other areas of the software, it is important for the change to be communicated clearly to all parties (hence the need for a formal process).
In addition to following the design, programmers in this phase should be applying best practices in terms of documenting the code they write as well as writing automated tests. This effort ensures that the code not only meets the specification, but that it works as intended, and is straightforward to maintain. Remember, the programmers working with the project during its maintainence phase will likely not be those who created it in the first place.