You need to be self-motivated, disciplined, industrious, resourceful and focussed.
Try to think of events in your life that demonstrate these qualities and make sure to mention them.
First of all, come up with a concrete idea of what they are looking for in a student.
Once you have this fixed in your mind, include a sentence or two that shows you understand this and that you're the person they've been waiting for.
As a general rule of thumb: Readability is a key factor in writing a successful motivation letter.
Even though you're addressing academics, it's best to keep the language as simple as possible. The professors may have to read dozens of these letters and want to find out about you as easily as possible, without having to wade through waffle, clichés or pompous-sounding sentences.
Microsoft Word has a handy built-in readability checker (based on the Flesch-Kincaid test) and you want the "reading ease" score to be between 60 and 70 points to hit the right spot. Even if you decide not to use half of it, listing all of these things out will give you some ideas of relevant skills you can mention.
A recommended overall structure for the letter is as follows: Before we move on to looking at the actual content of your letter, just a quick note that should really go without saying – stick to the facts. Another mistake people commonly make is to list their skills without providing any evidence, or just generally making vague statements. Give an example: “During my time at XYZ Construction Ltd, I worked closely with various team members to plan and build a gherkin-shaped tower block”.
A good example of this could be if you have worked on any relevant community or voluntary projects.
A Ph D is very different from undergraduate and postgraduate studies and requires different skills.