The term "reality based" has become a battle cry for progressives ever since an exchange between a White House lackey and a reporter, in which the White House fellow tried to make the point that they shaped their own reality, instead of responding to the one in the outside world like reporters do, came to light.
It sums up everything that is right about liberals. We do care about the evidence. We do care about the facts. It isn't just politics. We listen to scientists opinions, rather than ignoring them. We look at social statistics. We would argue that it is no coincidence that the people who make their living gather facts about social issues, academics and reporters, tend to be liberals. We want policies that work, not policies supported by the Bible or any other myth.
Being "reality based" provides a direction for resolving disputes. Disagreements over the facts can be resolved by presenting evidence. If you are reality based, it is your obligation to concede to someone who disagees with you when the facts show that the other fellow is right, and you are wrong. It also implies that you reject the idea that the press or science or academia has some mass conspiracy to lie to the world.
Of course, not all disputes can be resolved strictly with the facts. Facts can be relevant to what you think about, for example, the abortion issue, but they don't ultimately resolve the definitional question of when life begins for moral purposes. Instead, they inform, without deciding, the process of going about choosing a definition that makes moral sense. For example, choosing a "life begins at conception" definition of life can have different moral desirability if 99% of conceived eggs produce live births in the absence of a decision to abort for reasons unrelated to the viability of the fetus, than it does if only 50% of conceived eggs produce life births in the absence of that intervention. Definitions should have some connection to the reason you need to define a word or concept, but ultimately, they are matters of preference and not matters of fact.
One of the frustrating things about this administration is that facts no longer matter, at least, they don't seem to matter. For example, one administration proposed Endangered Species Act rule (whose fate may be tied up in a vote on the act taking place in Congress today), would call for classification decisions to be made on 1970s science, ignoring everything that has been learned since then. How idiotic!
The other frustrating thing about the political scene in this country, is that it is increasingly no longer sufficient to reach agreement on the facts to reach a decision, but the moral landscape of conservatives has changed so profoundly in the past several decades (far more than that of liberals). Once upon a time, Americans agreed that our nation should protect human rights and civil liberties. Now, you will increasingly hear conservatives say things like: "Even if we are torturing people or sending them to be tortured, what is so bad about that?", or "We don't care if the guy can prove himself innocent of enemy combatant charges, we're so afraid that we are willing to give the President power even if he can absue it." Civil political debate is basically about persuading people about the facts so that common ground can be reached. But, when there is no common moral ground, and that is increasingly where we stand today, debate inevitably disintegrates and dissolves into name calling, vitrol, and hard ball political tactics.