Questions & Answers about Мне нужно кое-что купить в супермаркете.
Because this sentence uses an impersonal construction.
In Russian, мне нужно... literally means something like to me, it is necessary... or I need to.... The person who has the need goes into the dative case, so я becomes мне.
So:
- я = I
- мне = to me / for me
This is very common in Russian:
- Мне нужно работать. = I need to work.
- Ему надо идти. = He needs to go.
Нужно means necessary, needed, or more naturally in English, need to.
In this pattern, Russian often uses:
- мне нужно + infinitive
- тебе нужно + infinitive
- нам нужно + infinitive
Examples:
- Мне нужно спать. = I need to sleep.
- Нам нужно поговорить. = We need to talk.
So Мне нужно купить... means I need to buy...