Doing something unilaterally means it's done without the agreement or participation of other people it might affect. A dad might decide unilaterally to take his family to Indiana for summer vacation, without asking them where they'd like to go.
You're most likely to come across the word unilaterally in a news report, since it's often used to describe actions taken by governments. If one country unilaterally launches an attack on another, it means the country's government does not consult groups like the United Nations or other affected countries before making the decision to attack. The Latin root, unilateralis, combines the prefix uni, or "one," with latus, "side," to make a word that means "one-sided."