The thoughts offered by Sonnet 60's speaker on the subject of time can be boiled down to two basic points. First: we're all completely at the mercy of time. We are born, we grow, and we ultimately all die, thanks to Time. Second? Time has no pause button. It just keeps on ticking away, no matter how much we could freeze frame any number of moments. Of course, as the speaker reminds us in the final couplet, even though there's no pause button, some things—like poems—are so enduring that they can last through the centuries, as if in slow motion.
Shakespeare uses the word "minutes" instead of "hours" to focus our attention on the little moments of time that pass by without our noticing—but all those moments add up.
Shakespeare personifies Time in the poem because he wants his speaker to have someone to fight against—and you can't exactly fight against an impersonal force.