Hey there,
Running out of memory can have a number of potential causes and it could be either system memory, video memory or even virtual memory/page file related. Without any of the information listed here, it can be tough to try and narrow down so I will offer some basics.
Make sure Windows is up to date. Manually check for updates. Then make sure you have the latest video drivers for your GPU(s) from the hardware maker.
You can also try closing out any web browsers you are using or going in and disabling hardware acceleration if it is turned on. (You can do the same for the Blizzard Desktop Application as well. See if that makes a difference.
You can also reduce the number of running programs on the system and see if that changes the issue at all.