Speaking means saying words out loud, the act of talking. Picture someone on the phone telling a friend about their day.
I was speaking to her for an hour. That is, I was talking with her.
Here is one more short scene to show the act of saying words out loud.
The teacher stood at the board, explaining the problem while the class listened. She was speaking, and everyone else stayed quiet.
It can also describe a back-and-forth exchange. On the bus, two friends quietly speaking about their weekend plans were speaking too, taking turns saying things.
This overlaps with the phone picture in the section above: one person producing words, or two people exchanging them. Both count as speaking in this sense.
A nearby word to keep separate: talk. The two often swap places, but speak can lean slightly more formal or purposeful, while talk leans friendly and casual.
I need to speak to the manager. Goal in mind, a bit formal.
We talked for hours. Just friendly conversation, no particular aim.