How can in increase downloading speed in my Linux system, I have two Ethernet interface on my computer with network bonding enabled, can I utilize both at the same time, Will it increase my downloading speed ?

Your download speed is limited by your Internet connection, not by the number of network devices in your computer. If you have for example a connection with 6 MBit/second even one ethernet card is far faster than that.

I had read this line on some sites
"Bonding allows you to aggregate multiple ports into a single group, effectively combining the bandwidth into a single connection."

Actually I am thinking that two different computers are connected with same switch, and download data (for ex) @250 Kb/s. then there should be some way that if I connect both cable to a single, it can download at double (2*250) speed. is it not possible ?
I enable network bonding, now I can connect cable to any of the interface it works well, so thinking to connect two wires at the same time.

No, it isn't. With bonding channels your computer is able to suble the bandwith within its own LAN, but not the connection speed from your modem/router to your ISP. Would be nice if that works, I would have ten network cards in my computer.

The ethernet card has a transfer rate at 10Mbits/s. The fast ethernet (which is more likely what you have) 100Mbits/s. Your Internet speed, I assume is at 250KB/s (aka 2Mbits/s). So, the network adapter isn't your bottleneck; even with an old ethernet adapter you can have that speed. If you need higher (Internet) transfer rate you need to upgrade your line subscription.
Of course you can try the bonding, but I think you won't get the results you expect.

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Well, yes you could bond two nics to improve speed on some networks between computer to computer and maybe some very high speed wan's.

You kind of get into some other limits but Intel is one company that tends to offer linux tools for their pro series to do such tasks.

A some point the lan tends to be faster than the computer. A cheap gigabyte nic can outperform backplanes and hard drives unless you have a monster machine.