Filibustering used to mean that you need a 60% vote to stop somebody from talking in Congress and you can not vote while somebody is still holding the floor so anybody who felt extremely strongly about a subject he (Or she) could simply walk up to the podium and keep talking. For example Strom Thurmond talked for over 24 hours straight in an attempt to stop civil rights legislation in 1957.
This kind of Filibustering kind of makes some sense to me. Not only is it fairly strenuous but you will also look like a complete idiot standing on the floor of Congress reciting the dictionary or your favorite recipes or anything else you can think of to keep talking so it comes with a definite cost and you wouldn't do it unless you were really passionate about something.
These days the rules have changed so now someone just has to say that he is Filibustering and everybody goes home. So unfortunately both Democrats and Republicans have started doing this almost as a rule for everything which means that you now need a 60% Filibuster proof majority to get anything through Congress since doing so really doesn't come with any real cost like it did before.
The fix for this is easy. Just go back to the old system of actually needing to perform the Filibuster and stand up there talking like an idiot. I doubt it will happen though since same as everything I've suggest before it would make the life of the people who needs to pass it slightly harder.