As @Jon Marshall notes, it's how you inform the switch, as a host, what gateway to use for non-locally connected networks. (Basically, the same as on a PC, when you configure its default-gateway.) (I believe you wouldn't need to use if if the local gateway device was doing proxy ARP.)
Since you mention "I have starting recap of Routing . . .", you might also have used or seen usage of a default route on L3 switches. That does for routing devices, much like default gateway does for non-routing devices. On a L2 switch, transit traffic is forwarded L2, i.e. no need for a L3 address. (Again, the default-gateway is for the switch, itself, as a host, to communicate with other devices on non-locally connected network.)
On a L3 routing device (i.e. L3 switch or router) the default route applies not only to locally generated device traffic, i.e. from the host device itself, but also to transit L3 traffic.
I recall (?) a Cisco L3 switch, when routing is enabled, default route will preempt default-gateway, but in theory, you could have both actively going to different next hops, i.e. again in theory, host generated traffic to default-gateway and transit L3 traffic to default route (assuming there's not a known destination network, or aggregate, better than the default).
