Well, I think they were just pointing out that there are two ways you must be prepared to have sex. Of course, the first is physical---you shouldn't be a child having sex. You should be a fully-grown man/woman.
By mentally prepared, the article is saying you have to be prepared in your mind---you have to be prepared with all the emotional aspects of sex.
A lot of people who lose their virginity too early regret it and were not "mentally" prepared to have sex. Even though they were physically capable, they didn't consider how they would feel afterward and some of them were not ready to deal with these emotions in a relationship.
Here's a comparison: sex is like driving---it isn't enough to drive the car and see where it goes. There has to be a mental preparation, and mental involvement with the act in order to make it best. You shouldn't be nervous or hesitant driving---the same goes for sex.
Emotionally, all sorts of things can come up with sex. You may feel weird or guilty or awkward, second guess yourself a lot - "was this the right choice, was it the right time?". It can take a while to sort out all the feelings that come up. Society, media, peer groups, family, church, ect. shove all kinds of ideas and images into our heads about the topic of sex. Your mind has to reconcile all that and make peace with it. After doing so, you are "mentally prepared" to have sex.
· 1 decade ago