Latency is the time it takes your data (packets) to get from point A (your house/modem) to point B ( the destination). Latency happens because of each of the "stops" your data has to make on the way to point B. These stops, called hops, are the different routers and in some cases servers across the internet that handles and routes traffic accordingly. The more hops that get added into the route of your data, the higher your latency will become. The farther away point B is, typically higher latency is experienced, simply because there is more distance and hops encountered. Also, each of these hops can also become busy so to speak, therefore the busier they get the more time it will take them to respond to your traffic requests, hence higher latency.
Most file transfer over the Internet uses TCP/IP. The receiver constantly sends messages back to the sender (ACKS) letting it know all is will or if not which packets need to be resent. If the channel has high latency this reverse communication take too long causing transmitter to stop sending until ACKS are received.
TCP also has a slow start mechanism. The sender has no idea of end-to-end channel capability. A slow start is designed to prevent overwhelming intermediate slower links.
Esentially, your bandwidth is the speed between you and your ISP, anything outside that, your ISP has no control over.
Actually, latency may or may not be an issue. Because latency is the delay between getting information from point A to B, it's much more of an issue in interactive applications then large transfers.
With large transfers, if your bandwidth is sufficient, reliable, and properly configured, you won't notice much of a latency issue with high latency connections. Once the "pipe is primed", the data is flowing at full speed. As long as the ACK packets are returned at a regular interval frequent enough that retransmissions don't occur, the flow will be steady and the only delay is really just during the initial startup of the transfer.
However, with interactive applications, that initial delay is what really can kill you. While it's exaggerated, say you have a 1 second latency and sending a packet takes 1 second. If you are sending a file that's 10 packets long, your total connection time is 11 seconds. If you are sending a single packet and waiting for a response back of a single packet, and you do this twice, your total connection time will be 8 seconds but yet you only sent 40% as much traffic.
Web traffic is kind of in between the two. It's not typically a large transfer, but it's not highly interactive like a online game. Typical page traffic is short bursts of requests (high latency) followed by longer periods of inactivity while you look at the page. There are a few tricks that can be done to help reduce this as an issue. There are proxy servers and pre-fetch utilities that will "preload" the page for you. During that time where you are looking at the page and your connection is setting idle, the prefetcher can download pages that the current one is linked to. When you request one, hopefully the page has been cached and can be displayed much quicker. If not, you are no worse off then having to wait for it to be loaded. This can work good for more static pages but if you are looking for something for dynamic pages (e.g. Google Maps), a prefetcher doesn't work as well or at all. Also, checking to see if your browser is using the appropriate number of connections can improve things.