Well it has two meanings. The first meaning of 'to groom' is to fix the appearance of a person or an animal for example. 'Well groomed' can be used to describe a person who appears to be dressed smartly. The second meaning is that it's an expression which means someone is taking advantage of another person by getting that person to like and trust them so that they could do whatever they want. Person A grooms Person B in order to abuse them sexually for example.
Many thanks for your answer @OldGeezer In the article I read, they were precisely talking about a "grooming network" involving many people. TO LURE was the meaning I was looking for. Another word to describe this would be the verb "TO BEFRIEND SOMEBODY" Thanks for your help.
@FRA-ENG-LEARNER You're welcome. Yes I would say that the second meaning is used the most in the media. I would say "to befriend someone" isn't necessarily the same as "to groom someone". The verb "befriend" quite literally means to be friends with someone. Of course someone could befriend someone to groom them but it's not always the case. I agree with "to lure".
Thanks for this clarification @AJEats You're right. The verb "BEFRIEND" doesn't imply that someone will eventually be groomed. It's rather a word that's often used to describe the "grooming process". But it's not a synonym. Again thanks for your clarification.