Example 1
Beth is finally watching all five seasons of The Wire.
The present progressive verb is watching denotes that Beth's viewing of HBO's drama (a.k.a. the best show ever made) is an ongoing action. She's likely watching it a few episodes at a time until she finishes the series, much to the delight of her friends and family who are sick of her covering her ears and yelling "No spoilers!" for a show that ended in 2008.
Example 2
This Sunday, Ian will be running in the Swamp 2 Swamp 5K to raise awareness for alligator dementia.
In this case, will be running is in the future progressive tense because Ian's participation in the charity walk is an action in progress. He's been collecting donations for weeks. Now if only he'd get off the couch and start hitting the gym.
Example 3
Amy had been pronouncing "chipotle" wrong for years before her new boyfriend, Josh, gently corrected her.
Poor Amy. Before she met Josh, no one had the heart to tell her about her mistake. That's a lot of burritos. That's also why had been pronouncing is in the past perfect progressive tense: she'd been saying it wrong for years.