In neutral terms, an activist judge is a judge who attempts to create law from the bench by changing laws to match a political ideology. While judges cannot legally create new laws (that power is reserved by the legislative branch of government at the state and national levels), they can clearly shape the interpretation of existing laws in a way that has an effect comparable to creating new laws.
In practical terms, people tend to use the term “activist judge” to refer to a judge who they believe holds a different ideology than the one they themselves hold. For example, some Republicans fear that Sotomayor is pro-choice and anti-gun. Hence, they are inclined to accuse her of being an activist judge because they think she might rule in ways they would disagree with. As another example, some liberals regard John Roberts as an activist judge because they interpret some of his rulings as being in accord with the Republican ideology.
One factor that often makes it easy to cast judges as activist judges is the fact that laws relating to controversial matters are generally imbued with political ideology right from the start. After all, laws are created by politicians and they tend to be rather prone to holding (or claiming to hold) ideological views. So, when judges make rulings on laws that are already imbued with ideology, their interpretations will tend to also appear (or actually be) tainted with ideological views. When a law is already politically biased, it can rather challenging to present a ruling that is free of political bias.
Another factor that makes it easy to cast judges as activists is that they interpret the law using their minds and their minds are obviously shaped by their experiences and values. While a good judge, like a good professor, tries to keep bias to a minimum, people make their judgments based on who they are. As such, someone who is a liberal will tend to judge in a liberal way. Likewise for conservatives.
The challenge is, of course, to determine when a judge crosses the line between being a human being with values that impact her view of the world and acting in a prejudiced/biased manner. It can, of course, be rather hard to discern what counts as bias. Part of the reason is that people tend to regard any ruling they disagree with as biased and any ruling they favor as being objective. For example, a conservative might see Roe v. Wade as a liberally biased ruling while a liberal would probably regard it as an objective and correct interpretation of the Constitution.
In the realm of practical politics, the Democrats and Republicans want to get people on the court who will support their ideology. A justice who does that is praised by her side and condemned by the other. So, it is hardly shocking that the Democrats are generally supportive (if not a bit over supportive) of Sotomayor while the Republicans are generally against her.
Ideally, of course, a justice should be the sort of person who will rule wisely in ways that are truly best for the country. Naturally, each side thinks that their ideology is what is best-and that is where the disputes get rolling.
My own view is that Sotomayor is a highly competent person. She has stood up well to the questions raised in the hearing, has a solid background in law, and seems to be a classic moderate Democrat-with the emphasis on moderate. I do not anticipate her making any “crazy” rulings or pushing ideology from the bench. She will most likely support Roe v. Wade against any challenges and rule in a way consistent with moderate Democrat ideology. In fact, I suspect that she will (like Obama) disappoint some of the folks on the far left with her views and rulings. Of course, once in a while justices turn out to be a surprise. But usually not.