From The news, Uncensored.
In general, you can divide the Jewish population here to four groups:
Ultra Orthodox (what they call here "Haredim").
This is a broad name for the very conservative (and some say reactionary) groups that go back to the time of the Enlightenment and emancipation of Jews in Western and Central Europe, where they as a response to the "Haskala" movement closed themselves up in their own community, and rejected many of the modern ideas. The very extreme groups among them reject the state of Israel, do not vote, and try to avoid the services of the state as much as possible.
The majority has tremendous contradictions in their connection to the state of Israel. On one hand, they vote and participate in many of the public aspects. On the other, they tend to view the state as a tool that is to be used as much as possible, and don't think much of democracy.
They are modern orthodox, and try to combine keeping the traditional Jewish religion to the t, and living and participating in all aspects of the modern life. Some of the groups here (like "Gush Emunim"), see the state of Israel as a messianic being, and thus tend to be among the extreme of the settlers in the west bank and Gaza. On the other hand, there are (admittedly much smaller) groups, which are very left wing, like "Oz VeShalom Netivot Shalom"
Literally, "masorti" in Hebrew means "conservative" but that is not a good translation, as they are very very different then the conservative Jews you will find in the US. Most of the people in this group is from non-European decent (mainly from the Middle East and North Africa), where the whole cultural approach to religion is extremely different then in European cultures. In many ways, it is folk religion. The result can look very bizarre to an orthodox Jew- they might kiss the Mezuzah every time they enter a room, keep kosher, but they would not go to shul regularly. Some will not light fire on Sabbath, but will happily drive to the beach on the same day.
Basically, non-observant Jews. The Spectrum here is very wide: you will find "Atheist Jews" who see Judaism as a culture only, people who just don't observe much of anything (but they do keep the major holidays) and any combination people can think about.
The Reform and Conservative movements are very small here, and have mainly Anglo-Saxon members. Most people in Israel due not consider then a viable alternative, and see them as forign.
There are many tensions between the groups above. The major one being between the Ultra Orthodox and the Secular Jews. I am sad to say that sometimes it gets as bad as mutual hatred.
The core, like anything else around here, is historical.
In brief- in the early days of the state, the prime minister then, Ben Gurion, signed a deal that let a select group of ultra orthodox young men to delay their compulsory military service, and study instead. In return, they will not allowed to work until they:
1. Serve in the army (if they are 29 years old, they get a shortened service)
2. Are 35 years old and are still studying
3. Have 4 children or more
Less then 30% of the people who use the deal do any service at all in the army (which is compulsory for everyone else).
The deal that was intended originally for a select few, grow enormously over the years. In 2001, 9.5% of the population for army draft in that year (those who where born in 1984) delayed (and in practice, canceled) their army via this deal.
Due to all sort of political reasons and deals, ultra orthodox that only study and do not work, get money from the state. If they have many kids, they get even more money.
This, combined with plenty of bad politics and bad economic, resulted in a large part of the workforce not working from choice, and receiving pensions from the state instead.
The "Tal Committee" was founded in order to find a solution to this situation. It's conclusion are still being debated today.
Another source of tension between these two groups is the disagreement about what does "Israel was founded as a Jewish state" mean in practice. Due to political reasons, this disagreement ended up manifesting itself in a series of highly debated "religious laws" and municipal laws a regulations, in attempt, every group from it's side, to shape the public arena.