To "request" something means to ask for something. To talk about the things that you ask for and count them, use the phrase "a request for ___":
My request for a transfer has been approved!
"Tech support" is short for "technical support". Most large companies have some employees whose job is to fix other employees' computers, install software, etc. You call this job, and the tasks that these people do, "tech support".
Putting these together, "requests for tech support" means the things that you ask for technical help with.