For your original question, Harlan has given you the answer you should use.
Kieran's answer cannot be used with full column references as it is an array
formula, however, given your last post, then it is probably SUMPRODUCT you will
need to do this, because that can take more than one criteria whereas SUMIF
can't (Which Harlan would also have told you had he been aware of the full
story).
Given your text then assuming your month was in a single cell as a number, eg 1
for Jan in say F2, then the following will give you what you need for each month
simply by changing the number in F2
=SUMPRODUCT((MONTH(A2:A10)=$F$2)*(B2:B10="YES")*(C2:C10))
If however, as per your example, you want to put a formula down col U and have
it calculate this data for whatever is in the corresponding cell in Col A, then
you need to lock the references, and make them of a size sufficient to cover all
your potential entries. You also need to reference the value in Col A instead
of a single cell in F2 eg:-
=SUMPRODUCT((MONTH($A$2:$A$10000)=MONTH($A2))*($B$2:$B$10000="YES")*($C$2:$C$100
00))
You can even make the ranges dynamic by using the OFFSET function if you like.
Personally though, despite all the above, I would probably use a Pivot table for
what you are trying to do - Much much easier and more flexible in terms of
reporting. Also, if you name the range 'Database' and then add records to it
using the form from Data / Form, the range will expand automatically to include
new records.
If you want an intro to Pivot tables, then try Debra Dalgleish's site:-
http://www.geocities.com/jonpeltier/Excel/Pivots/pivotstart.htm