The body of a good covering letter would read along the following lines:
1. Why you are writing
Open the letter with why you are writing.
Mention the advertisement if you are applying in response to one.
2. Introduce yourself
A quick summary of what you are doing now and have done/achieved during your career so as to give a quick snapshot and background.
Focus on the key aspects of your career narrative and seek to create a relevant hook for the reader so their interest is peaked.
3. Why that role/firm/organisation?
This is where you show that you are not just applying for jobs and to firms/organisations in a scatter-gun fashion.
Avoid using generalisations here - be specific about appealing aspects of the firm and role and tell them why those things are important to you.
Seek to back up your reasons and personalise them by mentioning how your work and other experiences have helped you make an informed decision to apply specifically to them.
4. Why you?
Highlight a particular quality you have and/or competencies or achievements of yours that show you have what they are looking for.
Focus on those parts of your experience to date that might help persuade them that you are the right person for them.
The key with a covering letter is to avoid just repeating lots of things that are already on your CV or elsewhere on your application form.
Instead, briefly mention a couple of the highlights from your CV but tie this into some reasoning as to why you feel you would be a good fit for the role/firm. It's about crafting a reasoned argument as to why you are right for this role/firm.
5. Sign off professionally
Thank them for their time in considering your application, state your availability for interview and ask that they contact you with any queries.
Do not waffle or go overboard here by stressing your desire to work for the firm or saying you want to contribute to the firm’s future success.
Help The Recruiter
Finally, as with all drafting in your job applications, be sure to help the recruiter by writing in a clear and concise manner.
Use short sentences and paragraphs in order to ensure the points you are presenting do not get lost in a sea of words.