Use this phrase when you're not quoting someone's exact words but the general idea. My manager mentioned we might get bonuses this year, or words to that effect.
Pro Tip 2/3
Unquoted Speech
Use to clarify that the speech is unquoted and may not be the speaker's exact words. She mentioned she's leaving soon, or words to that effect, but didn't give a date.
Pro Tip 3/3
Reported Speech
Often used in reported speech to summarize what was said without quoting word for word. The teacher said the homework was important, or words to that effect.