Firstly, it's important to understand who allocates each address space. PI (Provider Independent) are assigned by a local RIR (RIPE, APNIC, AFRINIC, ARIN, etc) to a Provider/Business/Entity. Whereas PA (Provider Aggregates) are allocated by an ISP/Entity to a customer.
With PIs, as the name suggests, the PI address space allocated is independent of a single ISP. The entity that has been allocated this space by the RIR can freely advertise this space anywhere on the Global Internet from their allocated ASN. One thing to note is that a PI must be in length from a /1 up-to a /24, nothing longer than a /24 will be allocated by a RIR.
PA's (Provider Aggregates) on the other hand are allocations performed by ISPs to their downstream customers. These can be anywhere from a /25 up-to a /32. These PAs will be allocated from a larger block that the ISP/Entity has received from its local RIR.