1. "Her favorite hobby, reading, transports her to different worlds."
* Reading is the gerund acting as an appositive, renaming the noun "hobby."
2. "The most important part of the plan, escaping, was executed flawlessly."
* Escaping is the gerund acting as an appositive, renaming the noun "part."
In both examples, the gerund clarifies or renames the noun it follows, adding extra information about the noun.