Struggling with explaining projects during interviews

1) Know your audience. Speak their language. Speak to their interests.
2) Give examples. Tell stories. These are engaging and memorable. They can set you apart from other candidates.

I would follow the PMI processes telling the story:
Initiating: What was the need and why
Planning: How your plan was detailed and accurate, and approved
Executing: How you successfully managed the project applying the PM experience you have, mention your communication and integration skills here
Monitoring and Controlling: I would mention any problem solving skills keeping the project in track.
Closing: How Stakeholders were satisfied with the final product and deliverables

Write what you’d like to convey, regarding your actions and successes, on several projects. Practice. Get comfortable with what you’re written. Then, don’t hesitate to refer to your document mid-interview.

I keep project notes in the front pocket of my interview professional portfolio. At least once per interview, I find myself starting to answer a different question with the same project or scenario. I pull out my list, scan it, and find the best project and scenario to fit the interview question. Your preparation and organization - and answers - will impress the interviewer.