The phrase often implies desperation or subservience, and is usually viewed negatively. As soon as the supervisor walked in, Mark started to lick his boots, losing respect.
Pro Tip 2/3
Metaphorical Use
It's used metaphorically to describe overly flattering behavior, not literal boot-licking. Sarah didn't actually lick her boss's boots; she just compliments him excessively.
Pro Tip 3/3
Informal Speech
Commonly used in informal situations among friends or in casual conversation. He's licking the teacher's boots to get a good grade, which everyone finds annoying.