The phrase often implies malice or intent to harm someone's reputation. After the argument, she began to speak ill of her friend to others.
Pro Tip 2/3
Confidential Context
It's commonly used in private conversations, not in the person's presence. Be wary, as some might speak ill of you once you're not there to defend yourself.
Pro Tip 3/3
Informal Tone
The phrase is casual and might be considered rude in formal situations. In the meeting, he spoke ill of our boss and shocked everyone.