On the 5th of March, Twitter is going to retire version 1 of its API. The replacement, version 1.1 is very similar, but with one major difference; every single call must be authenticated.
This means that come March, your existing API calls will break; including simple things like displaying tweets on your site. To fix this, you need to move to the new v1.1 API, and authenticate with Twitter.
Let's look at how to do this in WordPress, by embedding a list of tweets on your site