I love hearing about how other designers work, especially with regard to the design process, as it's one of the most important parts of our job. If I were to prioritize the importance of what I do,  I'd say:
(1) design process, (2) record/bookkeeping, (3) project management.  

And here's my thought about this--as with any business, the "business" part of what we do as Interior Designers is important...really important. Without a proper handle on the biz component (customer serv., vendors, invoicing, marketing, etc), it's impossible to plan, strategize or grow. But if the basis of your business is design (or photography, or cooking, or writing...or whatever, really), it's so important that you're good at the service itself, because everything else stems from that. So I think the design process is the most interesting/important part of what I do, and I find that I continue to refine my personal process each time I meet with a new client. Using a mix of interviews & images, I hone on what my clients are attracted to visually and listen closely to the verbal clues that pepper their conversation (words like mix, bright, open, cozy, clean, light) as they discuss their dream space.  Sounds simple, but I'd say my job is part psychologist, part audiologist, part nanny, and part relationship counselor--interesting mix, right?
Check out this Architectural Digest video of Vicente Wolf discussing his creative process of over 30 years...

(I had some trouble with this video yesterday...if it's not loading, click the link above!)