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What should they achieve, if anything?
They are very important. In terms of M.Arch applications, in MOST cases (not all), your portfolio, letter of intent and your recommendations stand as the 3 most important parts of your application. That is followed by your grades, GRE, experience, etc.
Recommendations can make or break your application. A lot of the schools look to your professors/bosses to acknowledge your stance and your background. For their letter, they will usually be asked questions such as "is this person capable of independent research," etc. Admission committees take these seriously.
If you are scrambling for recommendations last minute, I have bad news for you. However, you can attempt to call/meet a professor in person and beg your case. Usually it is common courtesy to allow them a few weeks, better a few months in advance to know/prepare/find time to write these things. Try asking past bosses/managers, and if it comes down to it, non-architecture/art teachers. Also, a very few schools (sci-ARC, for example) allow letters to be sent a few days PAST the due date of the application, as they understand that these letters are not in your hands but in the hands of your recommenders, thus your not held responsible.
Hope that helps.
Basically what kind of a person/student you are, whether you have potential, and that sort of thing. Grades and achievements do not fully embody an individual and these letters from people who presumably know the applicant provide an intimate perspective.
I've done recs for my students before. Don't mind last minute cuz I always do them last minute anyways. I recycle the same glowing letter and they always get in, even in the case if the guy, where I forgot to change the "she's" and "hers" to "his" etc. proud to say that guy got into his first choice school and is rocking it right now. Probably had nothing to do with me :)