Normal Layer 2 only switches can only send and receive packets to ports that are on the same VLan/network. If you have 2 computers that are on 2 different networks: IE 192.168.2.xxx and 192.168.10.xxx the switch would have to send those packets destined for the other network to a router which would then resend those packets back to the switch on the correct network.
A layer 3 switch is able to do this on its own without the need of a separate router. This increases speed, especially if the router is several hops away. The packets don't have to travel as far on a layer 3 compared to a layer 2 when crossing over to another vlan/network.
Think of it as riding one bus and needing to transfer to another bus on a different route. Instead of having to ride the one bus all the way downtown (router) to get on the other bus you can change buses at the local bus stop (Layer 3 switch).
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