Ashkenaz or Ashkenazi Jews are Jews whose families originally came from Eastern Europe - places which are now part of Germany, Poland, Hungary, Russia, the Baltic States etc. (The word Ashkenazi comes from an old Hebrew word for Germany).
Although all the underlying laws are the same across Judaism, Jews from different countries have different customs in the details of practise and pronounciation of Hebrew.
The main other group is Sephardi, for Jews who come from Spain and Portugal (Sephard is Hebrew for Spain). There are also more customs from the various middle-eastern countries, and also Italy has its own customs!
Most Jews in the UK are Ashkenazi, on the other hand, most French Jews are Sephardi (due to them coming over from Spain and north Africa).
Culturally, the various groupings of Jews have all absorbed things from the local regions they originate from. Ashkenazi Jewish cooking is based around heavy meat and root vegetable meals, as would be popular in Poland. On the other hand, Middle Eastern Jews tend to eat couscous, falafel and other things that would be popular in that part of the world. This is reflected in the different foods used for the rituals as well.