Being a tester one should never ever work in an isolated environment. He should be aware of whole Product functionality and architecture.
For starting you may proceed with -
1. Learn to login to the ip where code is deployed and check the logs to understand why a particular test case is failing.
2. Checkout the code in your machine and go through the code of the functionality you are testing. You might not be able to understand everything at first but keep trying. It will benefit you in two ways, one you will avoid unnecessary testing, you will know where the code can actually break. Second it will enhance your test suite from the extra test case you will write to cover all the paths of the code.
3. Always be part of design sessions there being a tester you can actually give inputs to product team that how user friendly the design will be.
4. Always try to find possible automation solutions if you are doing manual testing.
These are the few things one should always be doing to keep himself in the game and be updated with thing happening in his company/industry.