“had a son.” This event about Mephibosheth seems to be inserted to assure the reader that the house of Saul had not been wiped out by the death of Ish-bosheth. Mephibosheth was still left. It also makes the point that David did not become king of all Israel by wiping out the house of Saul, because we learn later that David took care of Mephibosheth (2 Sam. 9:3-13).
The fact that Jonathan had a son also makes the point that he had a wife, and it is noteworthy that nothing at all is said about what happened to her. In much of the biblical record the wives are in the background, as in the record of Jonathan.