What it is
What is a Motivationsschreiben?
The short answer
A Motivationsschreiben is the letter of motivation German-speaking programmes ask for: one page, roughly 400 to 600 words, formatted as a formal business letter with addresses and a date. It stays close to module-level academic fit rather than narrative, and it is markedly more formal in register than a US statement of purpose.
It is a letter, and the format is part of the assessment
Your address, the institution's address, a date, a subject line, a formal salutation and a formal close. A US-style essay pasted under a German heading reads as someone who did not check the convention, and convention carries more weight in German admissions than applicants from India expect.
What goes in the one page
Which programme and why that one specifically, usually by naming modules or a specialisation. What in your degree prepared you for it, with the mapping made explicit. What you intend to do afterwards. Brevity is expected rather than penalised.
Some institutions also expect a photograph and date of birth on the accompanying tabellarischer Lebenslauf, which UK and US conventions omit. See APS and uni-assist for the documents that travel with it.
Related questions
How long should a Motivationsschreiben be?
One page, roughly 400 to 600 words. German programmes treat the one-page convention as a real limit rather than a guideline, and a two-page letter signals that the applicant did not check what was expected.