When you condole, you express your sadness at someone's death. Sending a "condolence" card is one way to condole with someone who has lost a loved one.
When my dog died, I found that other dog owners were more likely to condole with me, since those friends who never had a pet had a harder time understanding how profound my loss was. There are many ways to condole when someone needs comfort after having suffered a loss. You can send a card, you can visit, bring food, or just sit with them as they grieve. If you've lost someone too, then you condole by showing empathy. If not, then you can condole by just lending an ear.