There's a lot of talk of "filibuster reform," but the Democratic proposal could be more accurately described as restoring the filibuster.
The Senate has traditionally permitted unlimited debate and discussion of a bill before the final vote was taken. As a side-effect this allowed senators determined to block a bill to talk it to death, since under Senate rules a 60-vote supermajority was required to pass a motion for "cloture" to cut off debate whenever even one senator wanted to keep talking. Prior to that a 2/3 vote was needed.
But in practice, for almost all the first 200 years of the Senate's existence filibusters very vanishingly rare. But both parties started making more and more use of them, leading up to current situation in which Senate Republicans have taken to filibustering almost every single bill of any significance, in effect creating an extra-constitutional requirement for a 60-vote supermajority to pass anything.
Moreover, the current "filibuster" is essentially the opposite of the traditional one. It's now necessary to get a 60-vote supermajority even to start debate. Then it takes another 60 votes in favor of a "cloture" motion to end debate before a vote on the matter itself (which needs only a majority to pass) can be taken, but in the meantime the Senate doesn't actually debate but rather does other things, unfortunately mostly routine stuff of little consequence.
A number of senators are behind a modest rule change that would restore the traditional filibuster by (1) ending the need for 60 votes to start debate and (2) requiring actual debating to sustain a filibuster, not a mere threat. (The last change doesn't even require altering the rules but simply enforcing them.)
It's disappointing that so many Republicans are reflexively opposed to such a small change whose effect would be restoring the traditional filibuster.
For more on the subject, see this post by Steve Benen.