Learn Hardcore Russian: Я прочитал конспект после урока.

Because конспект is the direct object of the verb прочитал. In Russian, direct objects take the accusative case. Since конспект is an inanimate masculine noun, its accusative form is identical to the nominative.

What does конспект mean in this sentence?

Here конспект refers to the set of notes or summary you make during or after a lesson. Think of it as your handwritten outline of what was covered in class.

What does the ending “-л” in прочитал tell us? How would it change for different speakers?

The “-л” ending marks past tense, masculine singular, perfective aspect.

A female speaker would say прочитала (adds “-а”).
For plural subjects (we/they) it becomes прочитали.
So you know from the ending that a man is speaking here and that he completed the action.

Why use the perfective verb прочитал instead of the imperfective читал?

Russian has two aspects: perfective for completed actions and imperfective for ongoing or habitual actions.

Я прочитал конспект means “I finished reading the notes.”
Я читал конспект would mean “I was reading the notes” (ongoing) or “I used to read the notes” (habitual).