Mario Apuzzo’s web site had a good explain/guess:
I believe it was a passport renewal application in 1965, because Obama’s family in Kenya says Stanley Ann (Dunham) Obama was there when Obama was born and government officials in Kenya state Obama was born there. Stanley Ann would have needed a passport in 1961 to get to Kenya and back to the USA. Since the 1965 passport was not in her 2nd marriage name when it was issued 4 months after her marriage to Lolo Soetoro, it is obvious to me she simply renewed her previously issued circa early 1961 original passport which was in either her maiden name or in the name of her first marriage name of Stanley Ann Obama, if issued after Feb 1961 when she is said to have married Barack Hussein Obama Sr.
A good explanation of the passport info (in the middle of the page):
Your belief is incorrect. Go look at the pdf's of the document for yourself. If you had done so, you would know that it is a renewal application filed in 1968 to renew a passport originally issued in 1965. There is no evidence she every held a passport before 1965.
because Obama’s family in Kenya says Stanley Ann (Dunham) Obama was there when Obama was born
Not a single member of his family has stated this.
and government officials in Kenya state Obama was born there.
One or two members of Kenya's parliament, who have no direct knowledge of his birth, have made off-hand remarks to this effect in political speaches. Given that these poeple have no special access to information about his birth, I don't see why you would assume they knew what they were talking about.