How to pass variables to awk command with conditions?

You have two basic choices: i) use -v to pass the variable to awk or ii) close the ' around the awk script, use the shell variable and continue the ' again.

1. Use -v

   while read city
   do
       awk -v city="$city" -F, '{
                                 if ( $1 == "ACTIVE"  && $2 == city ){print $1}
                                }' siteDBName >> count
   done < city_name
   

2. Close the quote

   while read city
   do
       awk  -F, '{
                    if ( $1 == "ACTIVE"  && $2 == "'$city'" ){print $1}
                 }' siteDBName >> count
   done < city_name
   

I removed the SUM= line since it wasn't doing anything useful given that $1 is ACTIVE so adding it makes no sense. See my alternate approach below for a way to do this correctly.

Also, note that with this approach, you need to read the siteDBName file multiple times. A more efficient version would be:

$ awk -F, '{
             if(NR==FNR){cities[$1]++;}
             else if($1=="ACTIVE" && $2 in cities ){sum++}
            } END{print sum,"active cities"}' city_name siteDBName 
3 active cities

Just as @cuonglm and @YoMismo stated, you are using the wrong variable and the wrong way to reference it. It should be something like:

while read city
do
        awk -v c="$city" -F, '{
                        if ( $1 == "ACTIVE"  && $2 == c )
                        print $1
                }' siteDBName >> count
        SUM=`awk '{ sum += $1 } END { print sum }' count`

done < city_name