It is slang derived from “何か(なにか)”. It has two meanings.
The first is “such“ and it is used to emphasize the noun that is put before “なんか”.
It is used to give an example, to be humble, or to look down on something. It is interchangeable with “なんて” in many cases. If you're inerested in “なんて”, please click HERE
The second is “kind of“. It is used to describe situations in which you feel/do something for some reason. You can use it while thinking about what you are going to say next or when choosing right words.
Ken and Leo are talking about learning languages.
- Ken: I’m thinking about learning foreign languages. I want to be able to speak Japanese fluently or something... because I like Asian cultures.
外国語を勉強しようかと思っている。アジアの文化が好きだから、日本語なんか(orなんて)…話せたらいいな。 - Leo: You can speak Japanese enough for everyday conversation, right?
日常会話程度ならできるでしょ？ - Ken: No way! My Japanese still has a long way to go.
まさか！僕なんか(orなんて)、まだまだだよ。 - Leo: Mike told me that he learned to speak Japanese fluently in just 3 months.
マイクは3カ月でペラペラになったって。 - Ken: What? How did he learn it? You shouldn’t believe such a stupid story!
はっ？どうやって？そんなバカげた話なんか(orなんて)、信じるなよ！
Meg and Amy are talking about what they want to eat for lunch.
- Meg: Do you think that there is anything light to eat at the ABC restaurant?
ABCレストランで、なんか軽い物を食べれるかな？ - Amy: Yes, you could get some sandwiches or something. I'm not so hungry, too. So we could go to another place if we can’t find anything nice there.
うん、サンドイッチかなんかあると思うよ。私もあまりお腹が空いていない。だから、何もなければ、他の店に行こう。 - Meg: Oh, I’m kind of relieved to hear that. Thank you.
あっ、なんかホッとした。ありがとう。
Meg wants to know more about Tom.
- Meg: Do you think that Tom has a girlfriend?
トムって、彼女(は)いるのかな？ - Amy: Why? Why do you ask me that?
なんで？どうして、そんな事を聞くの？ - Meg: Um...I don’t know why, but I kind of like him.
んー...よく分からないけど、なんか彼が好きかも。