1. Author has a unique personal perspective (background knowledge, historical insight, whatever).
2. Essay has a striking thesis, and defends it well.
3. Author is a big shot, and it's useful to know what they think.
There's undergraduate work that meets criteria (1) and (2) --- but it's rare, and effectively lost amid the ton more than that that doesn't. To attract repeat business, you've got to attract the good stuff, and establish filters which separate it out. Around here, the problem of attracting the content is called the "chicken-and-egg problem", and Google will turn up some discussion.
Two further thoughts: First off, the pointers to the essays should state a thesis. As I write, the top one analyzes "the cause of piracy and the solutions available to the International Community ... using several concepts that are relevant to the failed state of Somalia ...". OK, fine (prolixity aside). He's talking about Somalian piracy. What does he have to say about it? If I don't know, I'm moving on.
Also, if you're trying to convince people your essayists' stuff is worth reading, there might be a better pitch than "undergraduate"; even "young" might work better.