The quick and dirty way to differentiate a browser from every other type of application (program) is that browsers have an address bar that entails "http" in the address. It is likely that no other application in a user's life has this characteristic.
The most common mixup is between Google and browsers. Add the fact that Google makes a search engine (Chrome) and you have a recipe for confusion. I explain that search engines are frighteningly intelligent and browsers are almost completely dumb.
Show the user that regardless of which Website they visit, the browser looks the same, ...except for the address bar. This affords an opportunity to reiterate that the address bar is the key unique feature of the browser. Moreover, if you gently nudge the user to utilize the address bar more (rather than typing URLs in to Google's search engine), this will likely lessen confusion about what a browser is and what a browser is for.
Try to be patient and give multiple analogies, even ones that aren't technically correct.
Feel free to share your experiences with explaining what a browser is to users.