The SUMIFS function, one of the math and trig functions, adds all of its arguments that meet multiple criteria. For example, you would use SUMIFS to sum the number of retailers in the country who (1) reside in a single zip code and (2) whose profits exceed a specific dollar value.
This video is part of a training course called Advanced IF functions.
Syntax
SUMIFS(sum_range, criteria_range1, criteria1, [criteria_range2, criteria2], ...)

=SUMIFS(A2:A9,B2:B9,"=A*",C2:C9,"Tom")

=SUMIFS(A2:A9,B2:B9,"<>Bananas",C2:C9,"Tom")
Argument name 
Description 
Sum_range (required) 
The range of cells to sum. 
Criteria_range1 (required) 
The range that is tested using Criteria1. Criteria_range1 and Criteria1 set up a search pair whereby a range is searched for specific criteria. Once items in the range are found, their corresponding values in Sum_range are added. 
Criteria1 (required) 
The criteria that defines which cells in Criteria_range1 will be added. For example, criteria can be entered as 32, ">32", B4, "apples", or "32". 
Criteria_range2, criteria2, … (optional) 
Additional ranges and their associated criteria. You can enter up to 127 range/criteria pairs. 
Examples
To use these examples in Excel, drag to select the data in the table, rightclick the selection, and pick Copy. In a new worksheet, rightclick cell A1 and pick Match Destination Formatting under Paste Options.
Quantity Sold 
Product 
Salesperson 
5 
Apples 
Tom 
4 
Apples 
Sarah 
15 
Artichokes 
Tom 
3 
Artichokes 
Sarah 
22 
Bananas 
Tom 
12 
Bananas 
Sarah 
10 
Carrots 
Tom 
33 
Carrots 
Sarah 
Formula 
Description 

=SUMIFS(A2:A9, B2:B9, "=A*", C2:C9, "Tom") 
Adds the number of products that begin with A and were sold by Tom. It uses the wildcard character * in Criteria1, "=A*" to look for matching product names in Criterial_range1 B2:B9, and looks for the name "Tom" in Criterial_range2 C2:C9. It then adds the numbers in Sum_range A2:A9 that meet both conditions. The result is 20. 

=SUMIFS(A2:A9, B2:B9, "<>Bananas", C2:C9, "Tom") 
Adds the number of products that aren’t bananas and are sold by Tom. It excludes bananas by using <> in the Criteria1, "<>Bananas", and looks for the name "Tom" in Criterial_range2 C2:C9. It then adds the numbers in Sum_range A2:A9 that meet both conditions. The result is 30. 
Common Problems
Problem 
Description 
0 (Zero) is shown instead of the expected result. 
Make sure Criteria1,2 are in quotation marks if you are testing for text values, like a person's name. 
The result is incorrect when Sum_range has TRUE or FALSE values. 
TRUE and FALSE values for Sum_range are evaluated differently, which may cause unexpected results when they're added. Cells in Sum_range that contain TRUE evaluate to 1. Those that contain FALSE evaluate to 0 (zero). 
Best practices
Do this 
Description 
Use wildcard characters. 
Using wildcard characters like the question mark (?) and asterisk (*) in criteria1,2 can help you find matches that are similar but not exact. A question mark matches any single character. An asterisk matches any sequence of characters. If you want to find an actual question mark or asterisk, type a tilde (~) in front of the question mark. For example, =SUMIFS(A2:A9, B2:B9, "=A*", C2:C9, "To?") will add all instances with name that begin with "To" and ends with a last letter that could vary. 
Understand the difference between SUMIF and SUMIFS. 
The order of arguments differ between SUMIFS and SUMIF. In particular, the sum_range argument is the first argument in SUMIFS, but it is the third argument in SUMIF. This is a common source of problems using these functions. If you're copying and editing these similar functions, make sure you put the arguments in the correct order. 
Use the same number of rows and columns for range arguments. 
The Criteria_range argument must contain the same number of rows and columns as the Sum_range argument. 
Related

The SUMIF function adds only the values that meet a single criteria.

The SUMSQ function sums the values after it performs a mathematical square operation on each of them.

See a video on how to use advanced IF functions like SUMIFS.