What you get with your android phone is a plain vanilla calendar app that you can discard in favor of better featured ones. Try these out:
If you want a feature heavy calendar app for android, aCalendar is for you. You can assign colors to tasks and events and the app goes easy on your battery. Importantly, it has QR code NFC barcode sharing, intuitive navigation and flexible recurrences. You can select fullscreen widgets for 3 view and even opt for moon phases and zodiac signs for birthdays. It builds on the native Android calendar and is available as a free and paid app, with the paid app allowing more advanced settings, tasks and choice of colors.
DigiCal gives you a choice of themes ranging from white to black but of more importance to power users is that it has customizable lock screen widgets and Google Now integration along with built in location search features. Notifications, as you will notice are considerably enhanced from the standard android calendar app. In addition, you can customize events, display calendar on a daily or monthly basis and sync with Google Calendar.
If you are a fan of the Apple ecosystem, then opt for the Sunrise Calendar originally built for iOS and now available in Android flavor. It has a clean and smart interface in addition to smart features like Apple Web calendar and Google Calendar support, ability to connect other apps and view all calendar events on a single timeline.
UpTo is similar to Sunrise in that this android calendar app allows you to view scheduled events on a single timeline. In addition, it has layers feature and allows users to customize the front and the back layers, allowing you to prioritize events. All you have to do is tap to bring up the contents. The layers idea is great for those with a lot on their calendar and helps you organize events into various categories.
If you want something more in your calendar then ZDCal is the app to download. It is not only stylish in terms of looks but it also has more by way of features and user-friendliness. For one, it has multiple views. You can swipe between views and switch calendars quite easily. ZDCal goes beyond a simple calendar in providing a period tracker for women and horoscopes. You also get cloud sync support.
For business users there is the Business Calendar app for android, a paid app with a host of features and the Jorte Calendar and Organizer.