If you have an urge to eat candy, you really want to eat those sweets. Your mother might urge you to wait until after dinner. As a noun, urge means a desire. As a verb, it means to strongly encourage.
Urge is related to the word, urgent, or 'pressing.' An urge is a pressing want, one that is almost a compulsion, like when you're so frustrated, you have the urge to scream. If you urge someone to do something, you feel strongly about it. You might urge a friend to wear an orange shirt not because you happen to like orange, but because they're walking in the woods during hunting season.