I have my HSA that is currently in savings or checking account. The Insurance company provides option to keep the money in Investment account.
What are the pros and cons of parking HSA fund in Investment ?
The idea is the same as how you treat money in a non-HSA account: "What are the pros and cons of investing money in my personal checking account?" The answer is in the long run you'll likely have much higher returns, and in the short run you have a much higher risk of losing a large chunk of your money.
Similar to how you probably wouldn't invest your emergency fund because you might need it on short notice, the same goes for an HSA- if you plan to spend it regularly, you probably shouldn't risk it losing value.
However, if you do not plan to spend your HSA funds for quite some time (because you can afford to pay your medical expenses out of pocket), then investing is a great idea. The HSA is one of the most tax advantaged products in existence in the US. You save on taxes when you contribute and growth is tax free (just like a Traditional IRA), but it's also un-taxed when you withdraw (like a Roth IRA) if you use it for eligible medical expenses.
If you do choose to invest it and not spend it for a long time, the best advice I can give is to save your receipts and document all your medical expenses so you can withdraw that amount anytime in the future, tax free.