It's not just means of production but also goods and services or really just about anything that's currently done for profit. Under communism there's no private education, no private Healthcare, no private infrastructure (no paying for internet access), no paying for food or clothes or a car. Your needs are met and you're free to do what you want.

If it sounds to good to be true, it's because it is. Communism is an utopia. It's not something we can realistically achieve, but it's a dream to strive towards. It's a dream of a better future.