What qualities are organizing committees looking for in a reference letter for a summer school? How would you write a reference letter for someone who is applying to a summer school intended for Ph.D. students/postdocs? The summer school only lasts for 3 days up to a week and I am curious as to what qualities and traits the organizing committee is looking for in participants. Do the participants have to be able to think very fast, for example?

What skills are sufficient to be able to participate in a summer school successfully? I am writing a reference letter for someone who is relatively new to a field and is interested in doing research on topics relevant to the summer school. The student has more or less the prerequisite knowledge needed for this summer school if that's worth mentioning. Also, the student is seeking for funding so I want to be serious about this letter.

From where I'm from, there weren't many opportunities for summer schools so I would appreciate your suggestions.

Thanks!
I once served as secretary for a summer school like this.  I wasn't directly involved with reviewing applications (this was the scientific organizer's job), but from conversations with him, my understanding was that the recommendation letter was intended mainly to verify that the student is a real person, is genuinely working in the field, and is at an appropriate level to gain something from the summer school.  Other than that, admission was not competitive (something like 90% of applications were accepted) since we didn't have any particular space constraints.  

I believe there were a few "junk" applications from people who were not grad students, or were in unrelated fields, or otherwise didn't seem likely to benefit from the summer school.  Some may have been confused about the summer school's target audience, or were cranks, or were not in the field but were trying to use the summer school as a way to get a visa to our country.  The recommendation letter served to filter out these applications.

(We also had some travel funding available, but it wasn't competitive either.   The funding came from our government and would only let us fund our country's citizens and residents, so we essentially just divided the available money equally among all eligible participants.)

So I would say the letter should include:


Obvious stuff: student's name, your name, institution, fact that you are the student's advisor (helps if the institution is well known, and/or if you are known to be working in this field).
Brief description of what the student is working on (e.g. thesis topic).  
Explanation of why the student is interested in the summer school.  If it is not obvious, explain how the topic of the summer school will be relevant to their research.  If there are specific connections, mention them.  ("One approach to Student's problem involves reticulated splines, so he/she is particularly interested in Professor Foobar's lecture at the summer school."  "Student has been recently studying Professor Barqux's papers on cromulent blobs.")
How far along is the student (just started in the program, several years in, about to graduate?). 
Do you believe the student is adequately prepared for the summer school, in terms of background knowledge?  If your program offers basic courses in the relevant field or subfield, has the student successfully completed them?  Give some assurance that the lectures won't be way over his/her head.
If you think the student is especially strong and their work is particularly promising, you could say so.  But I don't think the organizers are looking for a detailed account of the student's academic strengths and weaknesses, or comparisons with other students.