A process server is someone who delivers court and tribunal documents ('process') in accordance with the rules of the particular court or tribunal. It can be their sole job, or part of their overall duties. Court bailiffs, for example, serve process.
If you ignore one, and they've made reasonable efforts to attempt service, you could run the risk that an order is made by the court or tribunal for an alternate means of service against you. This could mean posting the documents to you, or affixing them to your property (just two of the examples).
What's important to remember is that the process server is just the messenger. They've got a job to do. If you've got a bone to pick, it's with the person pursuing the action.