Strong interpersonal skills can help you during the job interview process because interviewers look for applicants who can work well with others. They help you understand other people and help you succeed in almost any task by adjusting your approach to working together effectively. For example, while a software engineer may spend most of his time working independently on code, he may need to collaborate with other programmers to effectively bring a product to market.
This is especially true as more organizations implement collaborative agile frameworks to work. Employers will look for employees who can both perform technical tasks with excellence and communicate well with colleagues.