I watched Himouto!Umaru-Chan and Umaru calls her brother Onii-Chan. Since Chan is a suffix after female names I was confused. At first I thought that it meant big brother, but I turned on a dubbed version and it still said Onni-Chan. So what does it mean?
You were actually right, Onii-chan means pretty much the same as Onii-san as in older brother. The difference is the former is informal or "cuter", while the latter is more formal, as "-chan" is an informal honorific, while "-san" is a formal one.
According to this short Japanese honorifics lesson:
This is an endearing female honorific. While it’s most commonly used for children, it’s also used fairly widely among family and friends
Chan is just a suffix used as endearment, most commonly for babies of both genders, pets, and girls or possibly women. Onii-chan is therefore an endearing way to say big brother, with a more feminine sort of sound. I don't think this is a typical way to call your older brother due to the feminine connotation.
In anime, however, there is a quite common trope often called "little sister complex" where it is considered "moe" or particularly "squee" for an adorable little sister type to call her big brother onii-chan. This can be in a cute innocent sort of way. See Card Captor Sakura for a cute, innocent example of this trope. Or it could be in a fetishy way. For example, I wouldn't be surprised if Daru in Steins;Gate has creeped on the girls in the show at some point by asking them to say onii-chan. As for how it applies to Himouto!Umaru-Chan I couldn't say as I haven't watched it.