"Palestinians" is an ambiguous term that has changed its meaning over the last century.
It used to describe the residents of the British mandate of Palestine before the creation of Israel, but nowadays it commonly referred to Arabs who has/had some ancestry in Israel before it's creation. Some people use it also to describe Arab citizens of Israel, while some don't.
The West Bank (a.k.a Judea and Samaria) is a region that was conquered and annexed by Jordan in 1948, then conquered and occupied by Israel in 1967.
Since 1967 Israel began to create settlements in the west bank, but most of the population in the area remained Arab.
In 1995 Israel signed the Oslo agreement, which gives the Palestinians autonomy in the West bank and Gaza, including civilian and security control in some areas.
Gaza strip is relatively small area conquered by Egypt in 1948, then conquered by Israel in 1967.
Like the west bank, Israel created some settlements there and gave it autonomy in 1995.
In 2005 following an increase in terrorist attacks from Gaza, Israel decided to withdraw from Gaza completely, uprooting all army bases and settlements, in hope to achieve progress in the peace negotiations, and at the same time, increase its legitimacy to respond to aggression from Gaza.
(Unfortunately, Israel's withdrawal was perceived as weakness in the eyes of the Palestinians, which, among other factors, resulted the rise of terrorist organization Hamas, which brutally conquered Gaza, and increased it's attacks on Israel until Israel responded in 2009 by what is known as operation "Cast Lead".)
The Golan heights are originally a Syrian territory, which was used by Syria to bombard Israeli northern towns with rockets and mortars. Israel conquered this area in 1967, and annexed it (its residents were given Israeli citizenship).
The 6 days war (also known as the 1967 war) happened after Israel learned that the Arab countries (Egypt, Jordan, Syria and Iraq) are coordinating an attack against it. Israel responded with a preemptive strike, and in 6 days was able to destroy the Egyptian and Syrian air-forces, conquer Gaza and the Sinai peninsula, the west bank and the Golan heights. (Sinai was later returned to Egypt in a peace agreement in 1982).
As to "why is there so much fighting" - it's a complicated question. At the basic level, most Arabs don't want so many Jews near them, especially as a sovereign country. To some extent - the "Palestinians" (in it's modern term) were created by the Arab countries when they refused to let the Arab refugees from the 1948 war to integrate into them, and kept them separated to use as leverage to pressure Israel. (These refugees became refugees after the Arab countries urged them in 1948 to leave their homes so they won't get in the way of their invading armies, set to destroy the newly declared Israel).
Israel is declared as the homeland of the Jewish people. It's a secular democracy, of which about 80% is Jewish and about 20% are Arabs (of which most are Muslim).