Opening a bank account

I imagine that they might be referring to the type of visa/permit that you may hold to allow you to reside in Kenya. 

I am confused though, as your profile says you are a Kenyan Citizen.

It certainly used to be possible to open a bank account as the holder of a single entry visa, provided that you had a referee who held an account at the same bank.  I understand that things have tightened up a lot and it is now much more difficult.

For investment, it might be best to look at investment funds such as Old Mutual rather than a traditional bank.

There is always M-shwari (part of M-Pesa) which has savings and loan facilities.  It is straight forward to register with them.