Syncing, believe it or not, is a very difficult mechanism to do well. Unfortunately, sometimes syncing doesn't happen as quickly as we would like. For example, when we create a new contact on your computer, we expect that new contact to show up on our phone almost immediately. It can be frustrating when that doesn't happen.
In most apps, there is an intuitive way to force it to re-sync with the server that it's connected to. In Mail, you simply pull down on your Inbox and let go. This will force Mail to check for mail. The other day, I had an issue with some of my events not syncing to my iPhone, so I needed to force a re-sync. It's not obvious how to do this like it is in Mail, but there is a way. This is how.
When you have your Calendar app open, tap on the "Calendars" link at the bottom of the app.
This will show you a list of calendars associated with your account. Now, pull down just like you would with your email Inbox to refresh the calendars.
This isn't the most intuitive way to re-sync your calendars, but it works!