What do lit agents do?

A literary agent can be many things, but first and foremost, they are your representative in the publishing industry. They negotiate contracts (book deals) with publishers who do not accept submissions from authors. In other words, literary agents are gatekeepers for the mid-to-heavyweight book industry.
An agent is usually an editor. The degree to which they will edit your work varies. However, they will typically recommend changes to help tweak your manuscript before it lands on the desk of an acquisitions editor.
Agents can also be coaches and champions. They've got your back in terms of the legal and business side of publishing, and they will ideally be an encouraging ally who will stick with you throughout a long career.
Agents may also be marketing experts, but that is not necessarily the case. Marketing is taken care of by the publisher, though the author is also expected to participate in this role—presenting at conferences and webinars, doing book signings, engaging with fans via social media, and more.
In exchange for their assistance, expertise, and connections, agents receive a percentage of their authors' earnings—usually 10-20%.