The term kaiken (kanji: 懐剣) means "chest dagger" in English. It is written かいけん in hiragana. It's pronounced roughly like "kigh ken".
This small dagger has the ability to be concealed in ones clothing, hence its name. 懐 alone is read as futokoro, meaning a kimono wearer’s chest area. This is where the kaiken would be hidden. You will find the kanji 懐 often used as the adjective natsukashii, 懐かしい, which roughly means nostalgic. Natsukashii is a common interjection; the English equivalent would be something like, “Wow that brings back memories!”
The other kanji in kaiken, 剣, pronounced variously as ken or as tsurugi (the Japanese reading), means sword. Though this is the ken used in kendo, 剣道, けんどう, it never refers to Japanese swords. Tsurugi means, generally speaking, European swords, while the word katana is used for Japanese swords.