The Immigration Department, which began operating in 1920, dealt among other things with registration and change of names and naturalisation applications and processes. In addition to files with correspondence on these issues, this Record Group contains about 50,000 files of naturalisation applications. These files contain photographs and forms with personal details from 1934 –1948, mostly submitted by Jews who came to Palestine legally. However, there are also some files of persons born in the country who applied for Palestinian citizenship.
For the most part, the files are family files, that is, they contain the application forms and photographs of the entire family, indexed by the name of the head of the family (generally the father).
Valuable genealogical material is also to be found in other files of the Record Group which deal with the issuing of passports, visas, laissez-passer documents and the registrations of tourists and immigrants arriving in Palestine. The material in this Record Group is not complete as the offices of the Immigration Department were subject to attack by the Jewish underground organisations, and many files were destroyed during these attacks. Moreover, British officials destroyed or took with them an unspecified amount of material in the final days of the Mandate.
Translation: people who applied for citizenship in Mandatory Palestine are likely to be in those files, along with their family members, locals who vouched for them, and various other charcaters who pop up. There are many tens of thousands of names, along with photographs, and lots of biographical information. And there's information about immigrants, information about the places they're coming from, information about how they began to fit in once they got here ... a wealth of interesting stuff.
Sadly, while the collection is now online, and most of it is in English (the language used by the British authorites), it is not yet easily accessable. The current interface of the ISA's main website was designed in the late 18th century, and if you know Hebrew it's a bit clunky and archaic; if you don't know Hebrew it's, well, more clunky and archaic. This will be fixed, hopefully, by 2015, but it would be cruel to promise anything sooner. Still, here's the list of the files, and if you use the חיפוש באוספי הארכיון button, the search engine will accept queries in Latin characters and will give reasonable results for this collection.
For reasons of privacy protection, files from less than 70 years ago are not yet online. But if you think about the history you'll understand why most people had either arrived by 1940, or they never arrived.