Cordial means warm and friendly in a sincere way. When your neighbor greets you with a cordial smile and asks about your day, she's being genuinely pleasant, showing real interest in how you're doing. A cordial relationship between two classmates means they treat each other with real friendliness and respect, even if they're not best friends.

The word suggests more than basic politeness. You might politely nod at someone you barely know, but a cordial conversation involves actual warmth. When diplomats from different countries have cordial meetings, they're respectful and genuinely pleasant to each other, even if their nations disagree on important issues.

You'll often hear about cordial relations between groups or organizations: two rival soccer teams might compete fiercely but maintain cordial relations off the field, or two businesses might be cordial competitors who respect each other's work.

When someone is genuinely glad to see you and shows it with warmth and kindness, that's being cordial.