I was just looking into this. What I've found is the following:

Code:

awk 'NR==FNR{a[$1];next}$1 in a{print $1}' F1 F2

NR==FNR -- this will only be true when in the first file
a[$1] use the first column to make array of file
next skip all the next blocks and process the next line
($1 in a) check in value in column on of second file
then print it

Code:

gawk 'FNR==NR {a[$1]++;next} ($2 in a) {print $2}'

So this is NR==FNR same as above
a[$1] s same as above
$2 in a -- is column $2 in the array of second file? then print it