The Plan

A Performance Improvement Plan is a formal document your employer gives you when they have decided you are not performing to standard. It contains goals. It has a timeline. It requires your signature.
The "performance" in the name refers to yours. The "improvement" refers to what the plan is supposed to achieve. The "plan" refers to a sequence of documented events that results in your termination if the goals are not met, and occasionally if they are.
(This last part is sometimes called "restructuring." The distinction is important to HR.)
The document usually begins with praise. You have been a valued member of the team. Your contributions have not gone unnoticed. The sentence after this is where the improvement begins.
You have ninety days. The goals are specific, measurable, achievable, relevant, and time-bound. HR learned this from a framework called SMART goals. The framework was designed for project management. Someone decided it also worked for the process of documenting that an employee was given a fair chance.
You sign the document. Your manager signs the document. HR keeps a copy.
This is what the word "plan" is doing in the title. You thought it was a plan for you. It was a plan for the file.