What is electronic harassment? How would someone prove it?

Electronic harassment is a general term that encompasses methodologies such as cyberstalking, libelous social media posts, threatening messages, et al. First, you have to research state and federal laws regarding their respective definitions of harassment and, if available, statutes on electronic harassment specifically.
One of the ways to document electronic harassment is to create digital copies of the media. For instance, if someone had sent you threatening text messages or emails, make sure you do not delete or edit any of the content. You can also utilize screenshot apps to preserve threatening or offensive social media posts/comments, so that you may have a copy of the contents even if the perpetrator deletes them. It is also essential that you do not edit or delete the metadata of any digital files you've created. In court, the opposing counsel can scrutinize any instances of manipulation you perform.
Once you've gathered your evidence, be sure to secure them in an encrypted folder or flash drive. This will not only safeguard the files from illegal extraction or destruction from malicious parties, but it will also preserve the integrity of the data.