This phrase implies a discreet interaction, usually for private matters or gentle reprimands. The manager is going to have a word in her ear about her punctuality.
Pro Tip 2/3
Quiet Conversation
It suggests a conversation that won't attract attention, maintaining confidentiality. I'll have a word in his ear during the break about the surprise party plans.
Pro Tip 3/3
Direct Approach
The phrase often means talking directly to the person involved, rather than about them to others. Instead of complaining to everyone else, have a word in her ear and sort it out.