Without more context it's hard to be certain, but usually stealing a line refers to a line of speech, like in scripts. It could be a joke, a reaction, greeting, or anything else spoken. It just means the person who says they are stealing it wants to use it in their own speech.

To steal a line in the context of my understanding would be.... Consider a great television program that you might enjoy watching such as "Friends" 'Superman' or 'Jurrasic Park" Now think of something someone said and you enjoyed the phrase. If you use the phrase, you can say, I was able to steal this line from the television show. I hope this is understandable. I would love to have you as a student and we can discuss many things further. Please check out my student comments and my profile. Then contact me in Skype for a FREE Class. priscilla0856

You need to provide more context. Where did you hear this?