Kafir is literally someone who buries a seed, and covers it.
In Qur'an, word Kafir is specially used for group of people among non-muslims, who have been rejected Islam after understanding it (and also group of people who took arms against Islam). Consider following ayah;
إِنَّ الَّذِينَ كَفَرُوا سَوَاءٌ عَلَيْهِمْ أَأَنذَرْتَهُمْ أَمْ لَمْ
تُنذِرْهُمْ لَا يُؤْمِنُونَ
Losely translated, this ayah says that it is same for "the ones who disbelieved" whether you warn them or not, they are not to believe. Notice that the word كَفَرُوا (they disbelieved) is in the past tense here. Hinting at the fact that they have already disbelieved and their disbelief is certain.
Moreover, see the following ayah;
مَّا يَوَدُّ الَّذِينَ كَفَرُوا مِنْ أَهْلِ الْكِتَابِ وَلَا
الْمُشْرِكِينَ أَن يُنَزَّلَ عَلَيْكُم مِّنْ خَيْرٍ مِّن رَّبِّكُمْ ۗ
وَاللَّهُ يَخْتَصُّ بِرَحْمَتِهِ مَن يَشَاءُ ۚ وَاللَّهُ ذُو الْفَضْلِ
In this ayah, Allah (c.c) talks about Kafirs among "people of the book" and polytheists. If all non-muslims were Kafirs, saying Kafirs from "people of the book" and Polytheist would make less sense. In this ayah, Allah (c.c) makes a difference between Kafirs and 2 groups of non-muslims.
So, kafirs are those people who have been made dawah for some time, they come to understand islam but decided to reject it anyways and are certain on their rejection.