Range = the values you want to compare TO
Criteria  = What you're looking for in that range
Sum Range = The range to sum if for the rows that meet the criteria

To clarify a bit, assume that you have the following data:

Cells A1:A10 - lists vendors from which you've purchased equipment (AT&T,
IBM, and Sun)
Cells B1:B10 - lists the cost of the items purchased.

Assume that there are a couple of entries for each vendor, and you want
totals for all three.

the formula to sum the AT&T values would be
=sumif($A$1:$A$10,"AT&T",$B$1:$B$10)

For the other 2 vendors, you'd simply replace "AT&T" with "IBM" or "Sun".  
The quotes around the names are necessary because these items are text values
(in this example).  You could also use a cell reference if the value exists
in a cell elsewhere.