Consider a situation where you wish to order something for the workplace, say copier paper.
In MM, you would create a purchase requisition. This would then per some workflow either get created into a PO directly or after the approval of a manager or more. Once the PO is made, it's sent to the seller. Now you wait until the seller sends you the products and they are received, at which point you do a goods receipt in MM. (Yes you may have Advance Shipping Notification, however that is overkill for little stuff like this.)
Now consider using SRM for this same function. In SRM, your vendor/supplier is more tied into the situation. So for example, when you want to buy the paper, you will directly see the vendor's catalogue, not your own material master. The order is programmed to travel directly to the vendor's system, and you can track the status much more easily. So while MM talks to the vendor via documents (PO, Invoice etc), SRM is much better integrated with the vendor's system, so you can be a lot more efficient in your interactions. The vendor will provide you with higher service, and you get a lot of bang for your buck.