Connections are always measured in bits. So your router can transfer at speeds up to 300 Mbit/sec. This has NOTHING to do with the speed of the Internet. It is simply the speed that the router can transfer information on your local network. Also, the router has little to do with the speed with which you can access information on the Internet either.
The maximum Internet speed at this time is 104 Mbit/sec using the DOCSIS 3.x standard. This speed is not offered in most places even where the HFC (Hybrid Fiber Cable) system supports it. Most places offer between 40 - 50 Mbit/sec. This is because you, the consumer, cannot easily utilize such a connection. Why is this you might ask? Why is it that I pay for a high speed connection yet you are telling me I can't make good use of it. Well, the fact is you are not likely to connect to a service on the Internet that will allow you to access information at those speeds. Just like you, the place you connect to has a bandwidth limit. They too are limited by the type of connection they have and the bandwidth alloted to them. Only difference is, they are sharing their connection with 100s, 1000s or even millions of users a day. In order to supply everyone with a similarly satisfying experience, they limit the maximum transfer speed from their servers to each user. That includes every resource on the Internet nearly without exception (encrypted traffic gets priority and can bypass normal limitations but is still subject to the limitation of the connection at the other end). It will be a long time before you will have the ability to transfer information across the Internet at the speeds your router is capable of on your local network.
That being said. I advise people pay attention to their actual bandwidth needs because most people are paying for an connection that far exceeds their use. Don't pay the cable company or FIOS provider for speeds you aren't going to use.