If you're being cheeky you're being brash or irreverent. If you're a cheeky child, you're probably just being impudent and disrespectful — and you're probably going to get in trouble.
Cheeky has shades of meaning according to the degree of offense taken, and this may vary between British and American English. At the offensive end are the synonyms rude, disrespectful, and insulting. Less offensive are sassy, arrogant, and shameless. Rounding out the cheeky spectrum are bold, assertive, and daring, which are about getting noticed but without causing injury.