What's the L3 SW ?

I have a layer 3 lab contains 4 L3 WS-C3560X-48T-S switch + Vlans.I can ping any pc from sw0 to sw1 but i can't which is weird ping any thing else like from sw0 to sw2 or sw3 , & i need to ask if we solved this issue then what is the purposes of the routing protocols if we can connect devices together via vlans. Thanks.
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