The EU (Germany in particular) invited much of the middle east in, then dictated to all of the EU members, that they NEED to take in some of them. To provide homes, benefits and so on. It really, REALLY didn't help when some of them came to the UK (as 'children') when they were clearly grown Men. That really rubs many people the wrong way. When anyone spoke out against it they were called 'racist' and got told that the poor migrants had a hard life hence why they look so much older than they 'really are'.
France have hordes of migrants, at the likes of Calais, whom attempt to board boats to the UK.
EU migration, as part of the EU immigration from the likes of Poland is more prevalent and easier done.
Many people voted thinking brexit would severely lessen migration from within the EU, toughen up the borders and also sever ties with the governing bodies of the EU. Many Britons feel the EUs leaders, such as Germany, are wallies who try boss everyone within it. Many feel that Britain puts in more than it gets out of it, if you know what I mean. The likes of Germany, UK, France prop up the EU and look after the smaller less able members. The people wanted all of Britains money and influence, to be directed towards it's own people, within it's own borders. In stead of helping people across the EU.
The British people want their governance dictated by the British government solely. They do not want rules implemented thanks to Germany, Switzerland, France and co'. This was almost like an independence vote, in a way. They wanted to severe the ties, they wanted more freedom and to be in charge of their own fate.