To repulse something is to repel it or drive it back. When you repulse your sister, you disgust her. When you repulse the enemy in battle or someone in conversation, you force them back or make them turn away.
Repulse is related to the word repel, and they mean similar things: to repulse an advance — romantic or warring — is to repel, or fend off, its advance. To repulse someone by being disgusting is to be repellent. You could repulse a person's attempts at conversation if you repulse him by picking your nose. Repulse is now most frequently used in the gross-out sense, but Jane Austin often had her characters repulse each others’ attempts at conversation or civility.