Hello Nazar, it's similar to "I agree" but its meaning and usage is closer to "Yes, I want to join or participate in that activity/group."
A: We're going to the movies this weekend. Want to come?
B: Sign me up!
But you would NOT use it to simply mean you agree because in many cases it won't make sense. For instance, if someone says, "I love fried chicken!" or "Star Wars is a great movie.", you cannot use "sign me up" as a response because there is nothing to join or participate in. Hope that helps.