What it means to assimilate?

Here is a question that people always ask and the politicians love to use it, be it here in the U.S. or overseas in Europe and other countries where there are lots of immigrants. What it means to assimilate is a legitimate question but what does it mean to assimilate truly into a society. Every time some terror activity happens in those countries, there is a serious debate about the alienation of the immigrant population and how there is a need to assimilate them into the mainstream society. Does assimilation means that I should be following whatever the native people are doing or I should have the same morals and standards and aspirations like them without compromising my actual identity. We should remember one thing that except for a few countries, every country had its native population which has been there before the immigrants. I have some examples to see that how the countries that cry out for assimilation has done different efforts to assimilate their population (there may be more but I will focus on a few briefly). Germany, one of the wealthiest countries in the world where it takes more time to become a citizen than ever. Germany has a big Turkish population which after so many decades still feels alienated from the mainstream. It maybe the fault of the Turks but they have not been welcomed either by the Germans too. Is it time to assimilate them into the population even if they have different religion?