Bananas are completely kosher for Passover. The term “kosher†refers to certain meats, fish, and even insects which are considered to be acceptable according to Jewish traditions. There are a number of foods which are considered to go against this sacred law and are therefore not allowed on this special occasion.
Bananas are a fruit though, so there is no significance or relation to kosher foods whatsoever. Those who are thinking about including bananas in their Passover celebration can feel free to do so; they are great for you and make for a delicious part of almost any meal at all.