How important is it to have a personal website, when applying for a PhD? I have read several questions regarding the importance of a personal website when applying to Posdocs and other academic jobs. However, I have found little stating the importance of it when applying for a PhD.
In general, how important is it to have a website as a PhD applicant?

In my case, I have done a bachelors and master in Chemical Engineering. However, now I am doing a master in Pure Mathematics and I am planning to apply for a PhD next year. From what I have read about admissions, the focus is on the SOP and the references, a website is hardly ever mentioned. These are the things I would like the admissions committee to know but might be too much detail for the SOP:


I feel it is important to explain why the change of fields. But I don't want that to cover much of the motivation letter. So I think of having a short post on my website explaining in detail how and why I changed fields. 
I would like to show how invested I am in the field (differential geometry). So I was planning on including a section with the conferences and schools I have attended during my master, and to showcase a student seminar I have organized at my university.  


I do not know how to put this information in my PhD application. So I think a website might be a good solution. Is this a good idea? what would be best for me to do?
The first of your reasons would be a negative, I think. It sounds defensive. This is not the impression you want others to have. 

The second of your reasons is not compelling. A personal website that just gives your qualifications is of little real value to anyone else. Your application materials will have all of that information in any case, so the web site is fairly useless. Additionally, the SOP is limited in length to get you to focus your writing on the important things, not to spew everything you know. 

However, a personal web site that has things to offer to readers to make their now lives and work better can be a very positive thing but more for later, when you are looking for employment. 

For example: 

In mathematics, a web site that had, among other things a set of challenging exercises that give insight when solved is a very useful thing. 

A blog that helps other students know how to learn a subject, or a topic. 

Book and article recommendations to people studying specific things. 

Software that enables generation of useful data or graphics or ...

If you can do something like that, then you can also have an extended CV with your papers and such as you develop them. But it needs to be more than just that if it is to really be helpful to others and to yourself. And if it is useful enough, then others will link to it, so that it starts to show up in Google rankings. 

You don't, of course, have to develop such a site all at once. It is an incremental task that requires only periodic maintenance over an academic lifetime.