what does "family name/given name" mean?

[grainna2003]

I came to the US from Ireland 36 years ago when I was 2. It has recently come to my attention that I need a new green card. I am married and do not know what to answer for "family name/given name" section of the I-90. Is "family"my married name and "given", my maiden name? Shouldn't my current legal name(my married name) be on this application some where?
Thanks for the help.

[immihelp]

family name = last name
given name = first name