Hello Ahmad,
That DSpace site you are showing appears to be a highly custom version of DSpace. You might reach out to them if you want specific information about how they've customized that site, if you want to see the same behaviors. The *default* behaviors of DSpace can be seen on our Demo Site at
https://demo.dspace.org/home (sample logins are available on the homepage).
At a basic level, the DSpace search filters (also known as "facets") are configurable on the backend using the guidelines in the "Discovery" Documentation (Discovery is the name of the DSpace search system):
https://wiki.lyrasis.org/display/DSDOC7x/Discovery So, this might be a good place to start to learn how to create new custom search filters in the sidebar. But, hopefully, whoever created that site you are referencing might also provide you with more hints on how they did that.
If you have more specific questions, feel free to ask them on this list.
Tim