I do not understand what exactly I should bring in the presentations section of my CV? In fact, during my Ph.D., I presented my papers at the conferences/workshops and internal presentations in my graduate-school colloquiums. Do I have to mention them in the presentations section or it is mainly about other sorts of presentations? BTW, I study CS.
The list of presentations in your CV is an indication of your direct, face-to-face engagement with your research community. All else being equal, researchers who give more talks are more visible/known/familiar to the community, which means their research has more impact.
Further, a list of invited talks gives an indication of your reputation within the research community. Again, all else being equal, researchers who are invited to give more talks are generally held in higher esteem, which means their research has (and will continue to have) more impact.
Giving lots of talks—especially invited talks—suggests strong communication skills, which correlate with well-written papers (which, all else being equal, have more impact), good teaching, successful grant applications, and effective public advocacy.
Finally, especially for younger researchers, a long list of presentations indicates that you know how "the game is played". Departments only want to hire junior faculty who show strong potential for earning tenure, which requires not only high-quality research but highly visible research. A list of talks in your CV signals that you know that your job is not just to sit in a cave and emit papers, but to sell your research and to make yourself a face in your research community.
Of course, these are all merely correlations and grace notes, and all else is never equal. A stronger publication record almost always trumps a stronger presentation record, so your CV should include your publications first.
[I'm also in computer science.]
In mathematics I have certainly seen CV:s with presentations and I have included them when applying for a position.
I have them divided as plenary talks (if I had given any), invited talks at conferences, contributed conference talks and talks at other universities, and finally talks at my own university (which I often leave off). I might also add non-academic talks, if I had given such.
I have even seen a list of attended conferences included, which seemed even less meaningful.
Plenary talks and invited talks clearly signal that you are seen as having something worthwhile to say, while contributed and institution talks do not require so much, but indicate that you are communicating your results to the wider community.
As a junior researcher, you might want to add these types of merits to the CV. You will want to leave out the less significant things off as your seniority increases.