Other forms: sacrificially
Anything sacrificial has to do with a sacrifice. Giving up your seat for someone else is a sacrificial act.
A sacrifice is something given up for the sake of others, so anything sacrificial is connected to that selfless act. In some cultures, people were once thrown in volcanoes to appease the gods: this was a sacrificial ritual, because the person's life was taken for a higher purpose. In Christianity, Jesus dying for other people's sins is a sacrificial act. Even small actions can be sacrificial if you give something up for a purpose.