acknowledge
To admit or show that something is real or true.
To acknowledge something means to recognize that it exists or is true, often by showing or saying that you're aware of it. When you acknowledge a friend's wave across the cafeteria, you wave back to show you saw them. When a teacher acknowledges your raised hand, she nods to let you know she'll call on you soon.
Acknowledging can be simple, like nodding when someone speaks to you, or more formal, like when an author acknowledges the people who helped with a book by listing their names in the front pages. In serious situations, acknowledging something means admitting a truth that might be uncomfortable: a student might acknowledge that they didn't study enough for a test, or a company might acknowledge a mistake in one of its products.
The word carries a sense of honesty and awareness. When you acknowledge something, you're not ignoring it or pretending it isn't there. You're facing it directly. Sometimes people say “I acknowledge that I was wrong” when they want to take responsibility for an error. An acknowledgment is the act of acknowledging something, whether it's a quick thank-you note or a serious admission of fault.