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what is the different layer 3 switch and router  ? please give me the clear definition and the real world mapping example

Switch = Roadpath
Router = Navigator
Layer 3 Switch = Roadpath + Navigator

Layer 3 switches generally routes faster than Routers (ASIC ability)
Routers have more robust routing functions

Layer 3 switches have layer 3, 4, 5, 6 or 7 (content) switching capability
Routers may have switchports also

From a functional perspective, there is none.  They both do the exact same thing. Which is to route packets from one network to another.

That said, there are some pretty significant operational differences.

Routers support dissimilar layer 1 and 2 protocols where layer 3 switches are ethernet only.
Routers typically have more features than layer 3 switches (VPN, NAT, etc.).
Switches are significantly faster than traditional routers.
Switches typically have a LOT more ports than routers.

There are many more differences but those are (IMO) the biggest.

If you need to connect for Ethernet LAN to another site over a T1 leased line or Frame-Relay, you will need a router.
If you have a large number of Ethernet LANs that need to be interconnected locally and speed is important, Layer-3 switch.
If you have to connect to the internet with an ISP provided Ethernet service but you will need NAT, you'll probably need to use a router as NAT usually isn't available on Layer-3 switches.

Let me to do summary between Hub, switch, router

Hub, that is device to connect all computers into network and data sent from one computer is transmitted to all other computers regardless of data target  destination.It is inexpensive cost,  and it operates in OSI model layer 1

Switch, that it s device appearance is like hub but more intelligent, forward data  to the destination that is a need to be connected to the network so that it will help to reduce network traffic in full-duplex mode. it is a little more expensive. and it operates in OSI model layer 2 with MAC address
 
Router that is one of example devices you can find it at your home router connecting to  your computer  through ISP to network. Also it acts as small computer and a lot feature inside.
You might try login  the router webpage by typing 192.168.0.10 on IE/Chrome browser and try its function such port forwarding  and disallow unauthorized access to the computers in the LAN from the outside Main difference on router to switch or hub.
In general,a router is explicitly designed to connect two networks together(LAN and WAN). A router also has additional "smart" software with security features that disallow unauthorized access to the computers in the LAN from the outside.When computer node is connected  to network, it will broadcast  its existing to the network and switch will pass what broadcast packet they have received to network, but Router won't do that
 Without the specific address of another destination device, Router  will not let the data packet pass through. Router operates in OSI model layer 3

There is a lot of articles about the difference hub, switch, router in google, and I just include those one that are easier to be understand and one link also including picture of the device
http://gonda.nic.in/swangonda/pdf/0789732556.pdf
http://www.webopedia.com/DidYouKnow/Hardware_Software/router_switch_hub.asp
http://askleo.com/whats_the_difference_between_a_hub_a_switch_and_a_router/

Example image to the role of switch and router:
http://3.bp.blogspot.com/_xh791ExUbh4/TTBG7885-cI/AAAAAAAAACo/mlxNgOZ6Qec/s1600/unmanaged_switch_and_hub.gif

Hope understand your question completely.If not, please pt it out

Duncan