See Syllogism : Basic structure :
A categorical syllogism consists of three parts:
Each of the premises has one term in common with the conclusion: in a major premise, this is the major term (i.e., the predicate of the conclusion); in a minor premise, this is the minor term (i.e., the subject of the conclusion).
The third term, that is not present in the conclusion, is the middle term.
A syllogism is of the first figure when the middle term is subject of major premise and predicate of minor one.
In conclusion, the syllogism :
No B's are C's.
All A's are B's.
Therefore : No A's are C's.
is of first figure (the middle term : B is subject in major premise) and is of from Celarent.
The major premise is "No B’s are C’s", that is C is predicated of no B's.
Thus C, the predicate in major premise, will be the predicate in the conclusion.
The minor premise is "All A’s are B’s", that is B is predicated of all A's.
Thus A, the subject in minor premise, will be the subject in the conclusion : "No A's are C's", i.e. C is predicated of no A's.
If you exchange the two premises, you get a Camenes syllogism in the fourth figure (added in the Middle Ages but already known to Aristotle) :
All A are B; no B is C. Therefore : no C is A.
The fourth figure is defined again through the middle term : a syllogism is in the fourth figure when the middle term is the predicate of the major and subject of the minor premise.