Congress has a bevy of rules relating to the budgeting process, so I’m going to simplify a lot and leave various things out.
Back in the mid-1970s, Congress found that it was necessary to exempt certain budget bills from threats of filibuster by creating a special process known as reconciliation, which limits the amount of debate on those certain bills. If a tax bill or a bill that would change entitlement programs (like Medicare) is afforded protection under reconciliation, there is automatically only 20 hours of debate on the bill, followed by an up-or-down majority vote in the Senate. Reconciliation doesn’t really matter in the House, because there is no filibuster in the House.
It is somewhat onerous to establish reconciliation protections for a bill. Both the House and the Senate must pass a budget resolution (that doesn’t go to the President for signature, and does not have the effect of law) that agrees that certain budgetary policies need to be changed. (These budget resolutions are also protected from filibuster.) So it isn’t like the Senate Majority Leader can decide on his own that a bill cannot be filibustered, he has to get the Senate AND the House to agree to that.
The reconciliation process is really only for budget related matters. Originally, it was thought to be only for decreasing the deficit, but there has kind of been a tug-of-war over time that has somewhat eroded that rule. Matters of non-budget policies (for example, changing laws on gun control or whatever) are excluded from the reconciliation process.
Please note that Condescending Robot is wrong. He has mistaken reconciliation for the “conference” process, which is entirely different.