Latency and bandwidth are related.
Bandwidth is a measure of potential - the transmission capacity.
Latency is a measure of delay - the amount of time it takes to get from sender to receiver.
"Throughput" is another term that's related, that I believe has to do with the actual amount of data getting through, as opposed to bandwidth which is more of a measure of potential. i.e just because you claim to have say 1GB bandwidth doesn't mean you're actually experiencing it.).
Here are several explanations that I've heard over the years:
If it's plumbing: bandwidth is the diameter of the pipe, latency is how long it takes a drop of water to get from one end of the pipe to the other. So in other words, your faucet might have a lot of water pressure (high bandwidth), but when you turn the faucet on, do you have to wait a few seconds for the first drops to get there (high latency)? It's worth pointing out that just because you have big pipes doesn't mean you use them to their full capacity all the time.
"never underestimate the bandwidth of a station wagon full of [hard drives] hurtling down the highway" - Andrew Tanenbaum. This quote is from a classic book on networks in which tanenbaum is contemplating the fastest way to send massive amounts of information from one side of the country to the other. If you fill a station wagon full of hard drives you could potentially send petabytes of information from los angeles to new york in a matter of days. Of course, it takes a few days for the first bit to get there (high latency) :). But once the first bit is there, the last bit is too. By contrast if you sent the same data over a network, the first bit might get there in a matter of seconds, but depending on the network speed, it might still take the last bit a few days to get there.
check my math:
1 petabyte = 1x10^15 bytes
1 gigabyte = 1x10^9 bytes
So assume you had a pretty fast internet connection, say 1GB / sec - this is a measure of bandwidth - with basically no latency so when you send a bit it gets to the other end almost instantly.
Then to send 1 petabyte from LA to NYC at 1GB/sec would take 1,000,000 seconds == 11.5 days.
If my station wagon with 1PB of data on hard drives would take, say 5 days to drive from LA to to NYC, then my station wagon has an effective bandwidth of 2.3GB/sec more than double your fast internet connection, despite the high amount of latency.