In the Houston metro area, people are usually referring to the grocery store. But since you are out-of-state, you should know that in the Dallas/Fort Worth area, HEB can also be a reference to the region that encompasses the cities of Hearst, Euless, and Bedford. The HEB area is just west of DIA (Dallas International Airport). So, depending on what area of Texas you're in, it could mean different things!
I have heard the word "heb" used by newcomers and it's a dead give away that one is not from Texas. It's not long before they are aclimated to say " H E B." Welcome by the way!
H-E-B stands for the name Howard E. Butts. The first H-E-B opened in Kerrville in 1905 by Florence Butt. 15 years later her youngest son Howard took over the operations of their grocery store business. In recent years, around the time of the store's 100 year anniversary, the grocery store chain ran a series of ads using the tag line "Here Everything's Better" . This is a link to the store's history, http://www.heb.com/sectionpage/about-us/company/heb-history/3000002