If you've got activity but no working connection on your Pi, you should look at your local network configuration, first by making sure your Pi is getting an IP address from your router, and then secondly from the Raspbian operating system itself. It is able to configure itself under almost any circumstances, but there are sometimes problems if your network is a little weird - you could be using two domains, for example, or a couple of routers.
The only way to solve these problems is to try to connect your Raspberry Pi to the simplest and most visible part of your network and then work your way back to the configuration you'd like to see. The final LED is used to indicate the speed of your network. If it's on, then your Pi has negotiated a speed of 100Mbps. That's 1,000,000 bits of data per second, or 100 megabits, otherwise known as a Fast Ethernet connection. This is a step up from the very basic 10Mbps indicated if this LED doesn't light, but it's still some way from the current fastest standard, which is 1,000Mbps, also known as a Gigabit connection.
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The reason why the Raspberry Pi doesn't support a Gigabit connection is because the Ethernet port is actually implemented through the USB 2.0 bus, and there's an upstream bandwidth limitation on USB that limits the potential speed of the Ethernet port to 100Mbps.
However, the connection speeds on the Pi are more than fast enough for almost every possible use, as it was only a couple of years ago that nearly every device featured the same amount of bandwidth. You're only going to suffer a performance bottleneck if you want to turn your Raspberry Pi into a high-performance NAS, or insist on streaming plenty of high definition movies at once.
Otherwise, the speed of the Ethernet connection isn't going to affect you, and you can just get on with enjoying your Raspberry Pi.