can someone explain persistence concept in detail with its types? not able to understand properly

Hmm little broad information. In short - persistence allows to forward the requests from the same client to the same pool member.

Let say your session requires authentication. You entered your username and pass. The current webe server holds this information. if your 2d request load balanced to the 2d pool member which has no login details you entered in the 1st pool member, you have to enter credentials again.

Persistence allows you to send the 2d request to the pool member which stores login data.

Every type of persistence depend on what you want to achieve and which options you have. E.g. you will not be able to use Cookie persistence for non-http traffic. In that case you will chose another e.g src ip based

You can read basics here. https://support.f5.com/kb/en-us/products/big-ip_ltm/manuals/product/ltm-profiles-reference-12-1-0/4.html

If you have any questions, feel free to ask