There are two parts to what will happen, UVa's response and the copyright holder's. For both parties: If you obtained the copyrighted material by illegal download or illegally copying someone else's disc, the you must delete any files on your computer that match the file name(s) specified in the violation notice we forwarded to you.
For UVa: You must REPLY to the original email we sent right away that the material has been deleted. If you don't reply promptly, your computer's UVa network access will be blocked. This means you will not be able to go anywhere on the Internet. When you open a web browser (e.g, Internet Explorer (IE) or Firefox) you will be re-directed to a Network Registration Block webpage, where you can resolve the issue by attesting that you have ceased unauthorized sharing of copyrighted material. Then your computer will be automaticaly unblocked within 5-60 minutes.
Even if you were unaware your activity was illegal, or if someone else used your computer to conduct illegal activity without your knowledge, you are still responsible for how your computer is used, and all the penalties described above still apply.
This is only part of the response - UVa's.
Copyright holders and the people who generate the violation notices can - and have shown that they will - prosecute you to the full extent the law allows. Here's a brief summary of the Civil and Criminal Penalties for Violation of Federal Copyright Laws.
Copyright infringement is the act of exercising, without permission or legal authority, one or more of the exclusive rights granted to the copyright owner under section 106 of the Copyright Act (Title 17 of the United States Code). These rights include the right to reproduce or distribute a copyrighted work. In the file-sharing context, downloading or uploading substantial parts of a copyrighted work without authority constitutes an infringement.
Penalties for copyright infringement include civil and criminal penalties. In general, anyone found liable for civil copyright infringement may be ordered to pay either actual damages or "statutory" damages affixed at not less than $750 and not more than $30,000 per work infringed. For "willful" infringement, a court may award up to $150,000 per work infringed. A court can, in its discretion, also assess costs and attorneys' fees. For details, see Title 17, United States Code, Sections 504, 505. Willful copyright infringement can also result in criminal penalties, including imprisonment of up to five years and fines of up to $250,000 per offense. For more information, please see the Web site of the U.S. Copyright Office, especially their FAQ's. You can also find out more at musicunited.org.
In addition, you should be aware that in summer of 2013, the U.S. Supreme Court declined to hear Mr. Tenenbaum's appeal, therefore making final, the federal appeals court decision to re-instate the original judgement in the long-running file-sharing case between Sony BMG Music Entertainment and Boston University student Joel Tenenbaum. The damages awarded were $675,000 for 30 songs, which is $22,500/song! You can read more at: Appeals court reinstates decision against Joel Tenenbaum and Wikipedia: Sony vs. Tenenbaum
A high school cheerleading student had to pay the Recording Industry Association of America (RIAA) $27,750! This is $750 a track for illegally sharing 37 songs when she was a high school cheerleader. You can read about her case and many others at: Wired articles about RIAA litigation.