complimentary
Given for free to show thanks or kindness.
Complimentary means given for free, without charge. When a hotel offers complimentary breakfast, guests can eat without paying extra. When an author gives you a complimentary copy of her book, she's giving it to you as a gift rather than making you buy it. Restaurants might offer complimentary appetizers to regular customers, and museums sometimes have complimentary admission days when anyone can visit without paying.
The word is related to compliment, which means to praise someone or say something nice. When something is complimentary, it's often like a gift that shows appreciation or respect. A business might give complimentary tickets to an event as a way of thanking good customers.
Be careful not to confuse complimentary with complementary (with an E). Though they sound identical, complementary means two things that go well together, like peanut butter and jelly. Complimentary means free. So complimentary peanuts on an airplane are free snacks, while complementary flavors are tastes that work well together.