I answered a similar question for a different firm but the main aspects of this question concerning innovation within the legal profession and choosing a business i admire remain the same.
The starting point would be to choose a business/person you are genuinely interested in. Don't write about something you think they would like to hear. The business/person you choose also provides some insight into your interests and personality so don't be afraid to choose something you are passionate about. This should help you answer the first part regarding why you find them innovative.
For the second part of the question, the key is to extract an overarching quality, strategy or aspect of that business/person and apply it to the legal industry. Law firms are ultimately a business driven to make profits so thinking in this way may help you construct your answer.
As an example, I chose a technology company from Asia and commented on how their business decisions were focused heavily on client experience and service delivery. I explained how this quality was particularly innovative because it goes right to the core of what innovation should be about. Innovation should concentrate on improving the client experience of services and not innovate just for the sake of innovation. I explained how this strategy provided the business with a structured approach in decision making, allowing them to allocate their resources in a purpose-driven way. I then applied this briefly to the legal industry whilst linking it closely with what the firm you are applying to could potentially do in the future if it adopted the same strategy. Always link it back to what the firm is already doing and comment on how the innovative quality you have chosen provides the firm a more competitive advantage.
