If your internet service is 1 gigabit or slower, then it won't improve your internet access.
Some ISPs are beginning to roll out 2 gigabit download speeds, and of course that is likely to spread. If you have that class of service, then multi-gig will certainly be needed for you to take full advantage of it.
Even if your internet service is slower than 1 gigabit, it will improve your access speeds within your home. I am using 10 gigabit ethernet now with my ReadyNAS and a desktop PC, and that does increase my large file transfer speeds from about 120 megabytes per second (~ 1 gigabit) to about 540 megabytes per second.
Internet speed it´s just one area to take in consideration ( even that there are some countries like Singapur where they already offer speeds beyond 1Gbps the average internet speed is below this 1gbps )
When we think about our network connection we have to think about other peripherals that are going to be connected to our network ( a 10G NAS, a 4k TV, a Blue-Ray player, an HD camera, etc..) and some of them are already beyond the 1Gbps speed.
Just take a look to any current latptop or desktop and you will see that most of the components are beyond 1Gbps ( SSDs are already at 5-6Gbps, USB it´s arround 10Gbps , WiFi it´s over 1Gbps too). The wired connection offers dedicated bandwith and the most reliable connectivity and right now using one gigabit it´s a bottleneck
