It has to do with the fact that Slovakia once belonged to the Austrian-Hungarian Empire (or Hapsburg Empire) for hundreds of years, starting with the XIth century and continuing until the collapse of the Austro-Hungarian Empire in 1918. In spite of this long history together, Slovaks have never become Hungarians and Hungarians on their part were never nice rulers... they always tried to transform any minority living in their country, make them lose their ethnicity (language, traditions, etc.) and become Hungarians themselves. Thus, many Slovaks were forced to fight for their rights and although they've been an independent nation for a while now, they have never forget their tragic experience with the Hungarians.
Moreover, Hungarians nowadays are still nostalgic about the former Austrian-Hungarian Empire when their country used to be much more important in Europe and much bigger in size. So they create problems in all the neighboring countries which have territories that once belonged to the Empire and where ethnic Hungarians are still living nowadays, as a minority: Slovakia, Serbia, Romania, Ukraine and so on.
So put yourself in the shoes of a Slovakian: after fighting for almost a millennium to preserve your ethnic identity, your language and your land against the Hungarian constant attempt to make you forget them, some minority in your country keeps dreaming about you losing your independence once again. This is the source of the tension between them.