To blur is to make or become unfocused and fuzzy. Crying hard can cause your vision to blur until you wipe your tears away.
Heavy smog or early morning fog can blur your view of the city, and two candidates' similar views can blur the differences between their political parties. In both cases, things become indistinct and hazy. You can also call the haze itself a blur: "The whole day was just a blur after the exciting news I got in the morning." In the 16th century, blur meant "smear on the surface of writing."