The 5th edition Player’s Handbook brings along with it what all other editions of the book did: classes, races, and options, so many options. The main difference of course is the differing rules system, the formatting (the appearance/look of the book), and who it was written by as well as how it was written.

Why Buy the D&D 5e Player’s Handbook?
The 5th edition Player’s Handbook has literally everything you require to make a character and actually play the game properly–unless of course you’re using D&D Beyond, with all the digital tools at your disposal. The book is one of the three iconic core rulebooks for Advanced Dungeons & Dragons (yes, Wizards just removed “Advanced” from the name by the time of 3rd edition AD&D), and so its needed to be able to create a character and know how the hell combat works in 5e.
Conclusion
That being said, unless you’re using online resources such as 5thsrd.org (an entire website dedicated the 5e SRD) or D&D Beyond, you most definitely need the Player’s Handbook maybe even the Dungeon Master’s Guide, though that’s for another post.
If you are playing the game on D&D Beyond, don’t buy the book digitally, its overpriced and a scam, just get a physical copy from amazon or your local (tabletop) gaming store. And if you’re just getting into the game either get the 5th edition Starter Set (for another post), which has pregenerated characters and a ready-made adventure, or buy the Player’s Handbook physically and play with your buddies via that.