The main tasks of a bioinformatician are programming software for data-analysis, actually analyzing the data, and further research to connect the computational data and results with the biology. However, as important is writing down the information for others (and yourself).
As a bioinformatician, the writing will be mostly documentation for the created software. Thus manuals such that others can use the software, comments in the code for other developers, and technical documents describing the software design process.
The pieces that are written from a research perspective are papers, posters, and similar documents. Here the focus lies on explaining the theoretical methods and the results gained from the performed analyses. Though it is great to have well designed and documented code, if it is not used there is no reason for the software to exists. Similarly, if the gained knowledge from the analysis is not preserved, why would one perform the analysis?
However, is knowledge truly preserved when no one understands what is written down? This is were writing skills show their importance. Creating a comprehensive story and understanding the audience you are writing for are the basic writing skills to learn.
Other writing skills include of course grammar and spelling. Though more important in my opinion is structure. How to organize the text such that it flows and connects. That it is ordered in a way that is expected. Many templates help with this, such as thr three- and seven-act structure for novels, or the standard setup of Introduction, Materials and Methods, Results, Discussion, and finally Conclusion seen in scientific papers.
Understand these structures, so they can be altered to suit the actual situation and needs of the knowledge that is being written down. Understanding the different structures will also help in creating your own templates for documents and aid in organizing the information from the start.
Though this is just the tip of the iceberg, these points are a great starting point to improve upon with regards to writing skills. Improving these skills will help in communicating better. It will likely also improve the general work of software development and research as well, as writing the information down forces one to think about it in more detail, while placing it in an overall picture. These two reasons shown again why writing skills are important to master.