Mariia, that's not what this means. It means to go somewhere with someone and sit down to a cup of coffee. For instance if you meet a friend on the street and want to have a chat, you can say "Do you want to grab a coffee (somewhere)?" It doesn't literally mean GRAB in the sense of taking it somewhere, it means to make time for it. Actually you can use GRAB in this sense with anything: You want to grab a game next week (=sit down and watch a game with me). We should grab a pizza sometime and catch up. (=go to a pizzeria and sit down and talk).

++Stas!