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How the internet speed is calculated, and how does it differ from other speed measurements (like CPU speed)? For example, what does it mean if somebody says, "my internet speed is 512"?

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Bandwidth is typically measured in bits per second (bps). Commonly used larger units are kilobits per second (Kbps), megabits per second (Mbps) and gigabits per second (Gbps).

It is important to distinguish between bits per second (bps) and bytes per second (Bps). One byte is equal to 8 bits. Most data measurements in computing are made in bytes and units of that, such as megabytes or gigabytes. Since network speeds are measured in bits, not bytes, a 10 Megabyte file will take 8 seconds to download on a 10 Mbps connection, not 1 second.

Internet speed measurement can be complicated by the fact that although you may have a high-speed link to your Internet Service Provider (ISP), you will then have to contend (share) the bandwidth with other users of the same ISP.

Handy tools for measuring bandwidth available include IPERF. Ookla develops a browser-based speed test used by some popular online speed-testing services like SpeedTest.net and SpeakEasy Speedtest.

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Technically, speed and bandwidth are two very different things. Speed is measured in latency/response time, not in bits per second. Bits per second is the size of the pipe, or how much data can move at one time. You don't measure the speed of a freeway by how many lanes it has, it just has a better chance of getting clogged with more cars on it when it has fewer lanes, just as an internet connection will slow down when you push more packets through than the pipe can handle. You measure latency on an internet circuit by sending pings to your ISP's primary DNS server (don't ping the default gateway as most often those routers are not configured to put priority on ICMP traffic).
This article discusses how speed on a processor is measured (clock speed). Memory is different, and is not measured in megabytes, as that is just the storage space where you can put data, memory is measured by the speed at which data is placed and retrieved from that storage. There are several different types of memory. Some types are that which is built into the processor (cache) and some that is inserted into the motherboard (RAM).
Also of interest might be the speeds associated with a hard drive, which include RPM (revolutions per minute), or how fast the platters spin, and read/write speed, which is how fast data can be read and written from the disc (which is not going to be the same through the life of the drive as various factors can affect this). RPMs do have an effect on the read write speed of course, but so does the number of platters (associated by the size of the disc) and the quality of the mechanisms that make up the drive head.

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