Moment magazine has a very interesting (and somewhat puzzling) list of people answering the question "What does it mean to be pro-Israel today?"
I would answer it a bit differently than the esteemed contributors.
An important Jewish concept is to be "dan l'chaf zechut," to give the benefit of the doubt. And if there is a distinction to be made between the pro-Israel and the anti-Israel crowd, it is that the former practices this dictum with respect to Israel and the latter tramples upon it.
When anything happens in Israel that looks bad on the surface, the vast majority of the time it can be shown to have been misunderstood or even fabricated. The psyche of Israelis is one of morality; while there might be exceptions one cannot fairly say that Israel is an immoral country. There is always another side to the story, one that sadly does not get the publicity of the seemingly bad one.
To be pro-Israel is to start with the assumption that Israel is right, and to be skeptical when things look otherwise. In the end, perhaps the explanation will not be satisfactory, but one needs to make the effort to at least find out what it is. If you are truly pro-Israel you would first do everything possible to find out the truth. That is what support means.
In short, being pro-Israel means treating it the way you would treat your own loving family.
It is a shame that some people who call themselves "pro-Israel" do the exact opposite - they take every sensationalist story out of the region as a priori proof that Israel is in the wrong. That is not "pro-Israel" by any definition. The excuse that they are doing it "for Israel's good" rings hollow when their antipathy is so consistent.
Being pro-Israel means that you are willing to be dan l'chaf zechut towards the Jewish nation.