What is the intent of 61.93(b)(1)? (b) Authorization to perform certain solo flights and cross-country flights. A student pilot must obtain an endorsement from an authorized instructor to make solo flights from the airport where the student pilot normally receives training to another location. A student pilot who receives this endorsement must comply with the requirements of this paragraph.
(1) Solo flights may be made to another airport that is within 25 nautical miles from the airport where the student pilot normally receives training

The student must be endorsed with something along the lines of:

I certify that (First name, MI, Last name) has received the required training of section 61.93(b)(1). I have determined that he/she is proficient to practice solo takeoffs and landings at (airport name). The takeoffs and landings at (airport name) are subject to the following conditions: (List any applicable conditions or limitations.)

Emphasis on the word TO, in (1). I interpret this as &quot;You must be endorsed to fly solo TO another airport for takeoffs and landings.&quot; However, my instructor, and it would seem the majority of the instructors at my school interpret it as &quot;You must be endorsed to fly solo AT another airport for takeoffs and landings.&quot; The FARs seem to imply my interpretation, and the recommended endorsement seems to imply the opposite (in fact the endorsement doesn't even mention the 25nm part except in title).
The situation it is used in most commonly is the towered-field TO/LDG practice. There is a towered field about 10 miles north of our airport where we all go to practice. However, the instructor is required to fly dual up there, solo the student, and fly dual back. Is this endorsement required in that case?
The intent of the regulation lies at the beginning, in 61,93(a):


  §61.93   Solo cross-country flight requirements.
  
  (a) General. (1) Except as provided in paragraph (b) of this section,
  a student pilot must meet the requirements of this section before—
  
  (i) Conducting a solo cross-country flight, or any flight greater than
  25 nautical miles from the airport from where the flight originated.
  
  (ii) Making a solo flight and landing at any location other than the
  airport of origination.


Training and an endorsement from an instructor is required before you fly cross-country or to another airport to land.  61.93(b) covers what the instructor must do with you before you can do anything specified in 61.93(a).

In the scenario that you describe you are not "Conducting a solo cross-country flight, or any flight greater than 25 nautical miles from the airport from where the flight originated" or "Making a solo flight and landing at any location other than the airport of origination" so subsection (b) does not need to be complied with at all.

The endorsement would only be needed if you were going to takeoff solo from your home airport, fly to the destination (which as you said is only 10 miles away), and land there since it is required by 61.93(a)(ii).