1 Gb RAM vs 10Gb application

RAM only load data which is operational (Being processed) at that time including buffer of some future data and old data if space available.
Like you are playing a video of 10GB with bit rate say 15Mbps. so idealy RAM should store only 15MB to which is being shown at monitor while fetching, but if space is there then it just buffer future data also.

Memory is sub-divided in two parts : 1) RAM 2) Virtual Memory.
RAM is the IC module, every motherboard has it's limit of RAM memory that can be extended.
Virtual memory, can be extended by using storage devices like HDD, SSD,etc.

Now, when any program is initiated, the required data is transferred to RAM from Virtual memory & when it is no longer needed then data is sent back to Virtual memory from RAM. This is called "Swapping"

Now consider your example, You have 1 GB RAM & the data you're accessing from HDD,SSD (virtual memory) is of 10 GB video file. Assume that video is full HD with 29.97 fps & consider that one frame is of 100 kb. Therefore, every second 29.97 x 100 kb = 2997 kb of data is consumed.

So, every second using swapping technology, 2997 kb of data is fetched from Virtual memory to RAM, & next second other 2997 kb is fetched & at the same time 2997 kb data which was fetched in first second is sent back to Virtual memory.
This process continues until entire video file is viewed.

Note that : When you access a file, not entire file is fetched by the RAM. Only necessary file is fetched & when it is no longer in use, it is sent back to Virtual memory.

Another small example, I have 512 MB RAM & I am accessing a game of size 700 MB. When I am playing game in a certain mission, only small part of game files is in use & not all. While I am moving on to other mission, other part of game file is used & not all. So, if game size is 700 MB, then also my PC with 512 MB RAM can run it.

This is only & only due to feature called "Swapping".