The Shabbat is a time concept unknown to non-Jews. Travelling to Israel gives you the need to coordinate your travel plans in or around this time slot. It starts at sundown on Friday (often with a dinner of the family) and ends on Saturday at sundown. During this time shops are often closed, you might not check in to hotels (though I never experienced this problem) and most major sights are shut down. Just like on Sundays in Germany, only from dusk till dusk.
The experience of restrictions according to Shabbat depend on whom you are with and where you are. In Tel Aviv you might only have minor problems, in Jerusalem it is worst for a traveller and Haifa is somewhere in between. When you have to do with orthodox Jews, it becomes interesting: They are not using any machines on Shabbat, the don’t press electric buttons, they don’t drive a car. In some hotels there are elevators that go automatically from level to level – so that nobody has to press a button.
It is kind of awkward if you are at Israel on Shabbat and in Ramadan (and outside of Tel Aviv): the Jews celebrate their weekly holiday, the Muslims do their daily fast breaking after dusk. Friday evenings can be very lonely in Israeli city centers.