Currently, in a 3-of-5 wallet, all 5 keys are treated as equals. While this may be fine for a majority of uses, it might not be best for all.
Imagine a system where a corporation has a multi-sig wallet with keys held throughout the financial management structure, the CFO's key should not be weighted the same as a manager's key.
While these systems are *technically* possible right now by just giving higher-weighted entities more keys (e.g. the CFO gets two keys, everyone else gets one), there is no real system for this in Bitcoin.
You don't need to give them more keys, you just have to modify the smart contract aka the script that is used to lock those coins up. For example in a 3 of 5 setup you want the CFO's key to have a "higher weight" then do something like this:
<CFO pubkey> OP_CHECKSIGVERIFY
OP_2 <pubkey 2> <pubkey 3> <pubkey 4> <pubkey 5> OP_4 OP_CHECKMULTISIG
This is a 3 of 5 multisig where the CFO pubkey and signature is mandatory and has a higher weight.