Vabruari is a portmanteau, a word that combines two others in both sound and meaning. The two component words are februari (February), and VAB, an acronym which stands for vård av barn (care of child).
Vab (vård av barn) is the name of a benefit paid out to working parents when they need to stay at home to look after a sick child, or accompany them to a doctor or hospital. It's a major part of what makes Sweden a family-friendly place to work, with parents entitled to up to 120 days each year per child (on average, they take around seven per child).
It can be written either as vab or VAB, and you'll see vabruari written as Vabruari or VABruari, but the most common form is all lower case letters (Swedish doesn't capitalize the names of months or weekdays). In Swedish, you'll hear it used as a verb, vabba (Matthias vabbar idag – Matthias is taking time off to care for his sick child today) and it's so common that you'll hear it used by English-speakers in Sweden too (Matthias is vabbing today). Not to be confused with vobba, which is a portmanteau of vabba + jobba, meaning to work while looking after a sick child.
But back to vabruari. With the year's shortest month bringing unpredictable temperature changes and the peak of the flu and vinterkräksjuka (winter vomiting virus), February has typically been the month when parents need the most time off to care for poorly offspring.
It has become a very common word, even if it's only been used over the past decade or two, and will be understood by anyone in Sweden; you'll even see it in writing at doctor's offices or from unions. Some brands even use it to advertise vitamins, puzzles or other products that might make the month easier to survive.
Vabruari är här igen – lycka till!
Vabruary is here again, good luck!
Februari kallas vabruari av småbarnsföräldrar eftersom barn ofta är sjuka
February is called Vabruary by parents of small children because children are often sick