This is a very complex question. I'll summarize the topic by saying that Jewish people believe that Israel is their original home (http://www.science.co.il/israel-history.asp). However, Palestine has been an established country since "the seventh century (A.D. 600's) when Arab armies moved north from Arabia to conquer most of the Middle East, including Palestine" (http://www.mideastweb.org/briefhistory.htm). So, you had a country that "belonged" to the Jews many many years ago. Then, the Romans took it over. Then, the Arabs took it over. And, then many, many, many years later, Britain stepped in and declared the Balfour Declaration stating that the Jews could have their land back. WWII ended, and Jews did not want to stay in the nation where they were persecuted and sent to death. So, they wanted their holy land back. Unfortunately, many tactics used during this "transition" were incredibly inhumane. Supposedly, this is a good starting point if you want to learn more: http://www.amazon.com/exec/obidos/ASIN/B00000IO04/metafilter-20/ref=nosim/
But, heed this warning, there is no topic that is probably more controversial and biased than this one. You will find pages and pages of what seems like trustworthy information that is objective, but it may very well only take into consideration one side of the coin.
I think lallalauren's answer is helpful, but I'd add that there has been a continuous Jewish presence in Palestine ? albeit small ? for virtually the entire period since the ancient Israelites were exiled.
Also, the majority of Israelis are Jews whose families came from Arab countries. Their roots in the Middle East go back for centuries. So it's a mistake to regard Israel as colonized solely by European exiles. In any case, it's a tragedy that the issue hasn't been resolved peacefully, especially given that so many on both sides accept the eventual inevitability of a two-state solution.