@KingCyrus:
I did a quick Wikipedia check to refresh myself, and I was mostly correct...
Essentially, the way it works is, in broad strokes:
1. All citizens are given equal civil rights BUT
2. Jews are given preferential treatment in certain issues such as immigration (which makes sense, as it was explicitly founded as a home for the Jews, and many of course immigrated first after the Holocaust and then after the War for Independence, even though of course many lived there before those events.)
3. The essential structure of the government is secular, it's not as if there's an overseeing religious body that makes it a theocracy, BUT
4. There ARE some Judaism-influenced laws, notably those pertaining to the Sabbath (I remember there was a big uproar when some stores sold the 7th Harry Potter book there on the Sabbath)...as in Prohibition America regarding alcohol, sometimes that's observed, and sometimes folks turn a blind eye, but there are laws that are religiously-motivated about the Sabbath, notably about stores and public transportation. There are exceptions to this, however; apparently Haifa, unlike most of Israel, has public transit on the Sabbath, as many there are Arab. Furthermore, the Chief Rabbinate has say over things that would traditionally fall under the old-old stuff of Jewish law, such dietary rules (ie, if you want your restaurant certified as kosher, you'd have to pass their rules to do so) rules of burial, etc.
5. There are therefore religious courts for handling disputes regarding those specific items, however
6. Regarding all secularized matters of life, including the basic governing of the state, that's all secular...that being said, you could always get a George W. Bush type as Prime Minister who decides that he or she really, really wants to emphasize the religiosity of the nation...but again, the actual electing and governing is secular, in theory and (mostly) law, anyway.
7. Aside from those minor issues of diet, burial, and other Old Testament remnants that the Orthodox Rabbinate really cares about, probably the two other areas where the religion would overlap would be marriage and education. As I understand it, there's something of a compromise between the secular government and the religious Jewish groups in Israel in terms of education, and that there's some overlap...the secular Ministry of Education handles matters, but there's again some influence from religious institutions (not, I suppose, unlike in England or parts of America, where if you send your kid away to a school in a certain part of the country, and it's religiously-funded or backed in part or on the whole, you're going to get some religion taught to you--that being said, there's still a common secular core that's to be taught regardless.)
Probably the most controversial area is gender and marriage. Intermarriage along religious grounds is at the very least problematic and possibly unrecognized/disallowed within the state itself (I'm unsure) BUT if you enter into an inter-faith marriage abroad and move to Israel, you're allowed to keep it. So, in a way, it's somewhat like what some would envision for gay marriage--your state may not allow it, but you can go to another state, get married, and have those rights retained in your home state, but you couldn't get married in that state. On the subject, gay marriage isn't allowed in Israel, and the age of consent for marriage is 17. Gender roles are...a long and complicated story. ;)
8. Finally, on the subject of religiously-recognized groups, there are at least five--Jews, Christians and Muslims (obviously), Druze, and Bahai. Other groups are recognized and allowed (like Buddhists) but those are the major ones. Each of those sects have their own religious ordinances to a certain extent over things such as marriage; however, to an extent, all of that is subject to the secular rule of the state.
There is no written constitution, but instead, the laws that exist at the present and a set of "Basic Laws" that govern how things work:
For starters, the Judiciary is independent of the Executive and Legislative branches, which both check one another. This is in part because of the aforementioned role religion plays in the religion-specific courts.
And section 1 of that Basic Law, which has been modified over the years, is as follows:
"Section 1: The purpose of this Basic Law is to protect human dignity and liberty, in order to establish in a Basic Law tile values of the State of Israel as a Jewish and democratic state."
From Wikipedia.
Without making this any longer, that Basic Law, which starts with that First Section, is the closest analogue to a "constitution" Israel would have, as those laws--really more declarations--are supposed to act as guiding principles that aren't to be breached or tread upon by a subsequent law unless the Basic Law is modified.
So, tl;dr:
1. They have laws respecting all citizens secularly BUT
2. Jews get preferential treatment on things like immigration AND
3. There is some religious influence in the Judiciary BUT
4. That's separated from the wholly-secular Exec. and Leg., which
5. Essentially ARE the acting government of Israel, while
6. There are multiple state-recognized religions, and
7. Obviously Judaism is the one with the most official and unofficial clout AND
8. That impacts things such as the Sabbath and what gets deemed kosher BUT
9. In MOST cases that doesn't conflict with/is reconciled with secular laws AND
10. Above all, Israel is intended to be a "Jewish and democratic state," wherein the democratic part is mostly secular but the cultural flavor of the nation is intended to be and remain Jewish.
...Hence why the 20% Arab minority in the country might feel disenfranchised (well, one of many reasons, but this is as long as this post shall go.) ;)