Although I don't think I've answered this question directly on applications, I think I have figured this question out through interviews/netowkring.
My best advice would be thinking for yourself, not about purely the 'Why Law' application approach like Jessica mentioned. Ask yourself, what is your personal USP (Unique Selling Point) or what makes you interesting? Rather than focus on why law (which may be important for applying to firms of course), consider three key things about you, that make you different or what you are personally proud of.
For me this would be:
- My background living an African country for two summers
- Because my culture is important to me and this experience taught me so much
- Being involved in volunteering society for secondary school students for 3 years
- My passion during university and something I worked alot on through different positions in the society
- My interest in the energy sector
- Because I have been reading more around the industry for past few months, whilst gaining some unique experiences from traditional oil company and emerging alternative energy start up
These are not directly about why law, they definitely could be, but they are a snapshot of me as a person/ professionally.
And this has definitely struck up conversations because law firms are interested in potential trainees from application stage to interviews. Applications and interviews always offer scope to discuss "Why Law", as it is vital for a potential employee to a firm, but make yourself recognised through these types of open questions. Of course if you had a key legal experience that makes you stand out or defines yourself professionally, mention it!
The main point is that for this example is reflect and highlight who are through this question. This took me years to realise but it is almost as important as highlight why you are entering the legal profession!
Hope this helps!