Emulate what you respect in your friends

Emulate - match or surpass (a person or achievement), typically by imitation."most rulers wished to emulate Alexander the Great"

Here is another example - "I do not wish to emulate her hairstyle"

So when it says "emulate what you respect in your friends" I think it means to tell what you would do that you respect in your friend - a trait or personality maybe?

something that you admire about your friends.