Its the frequency to which the CPU operates. The more "gigahertz" the more operations per second. 1.8ghz means 1,800,000 CPU cycles/second (clock cycles), whereas 2.4ghz is 2,400,000 cycles per second. Generally, the faster this number is the faster the computer will operate.
There were two MASSIVE exceptions to this rule in recent history however:
1) Apple's use of PowerPC chips which were "RISC" based (Reduced Instruction Set Chip) whereas Intel chips are "CISC" (Complex Instruciton Set Chip). A RISC chip can do far more work per cycle due to the "better" engineered instruction set. Chips now are so fast/powerful that CISC works damn well for consumer use. For a good, yet basic overview:
http://cse.stanford.edu/class/sophomore-college/projects-00/risc/risccisc/
2) AMD Athlons vs. Intel Pentium 4. This is when AMD changed over to the 2400+ type nomenclature. It was because an AMD running at a clock speed of 2ghz could do the work of an equivalent Pentium 4 with a clock speed of 2.4ghz (example, maybe not the correct speeds exactly) This was because the Pentium 4 was horribly inefficient and needed multiple clock cycles to do what the AMD could do with less clock cycles.
This is the primary reason Intel more-or-less left the Pentium4 style CPU cores behind. The early "Centrino" chips in laptops spanked the P4's of the time. A 1.8ghz centrino would top a 2.6ghz P4 in many respects, despite the Centrino chips of the day were actually re-engineered Pentium3 type cores.
As far as for computers now:
-L2 cache is WAY important. This is why the AMD Turion64 X2's get torn apart by the Core Duo/Core 2 Duos, because the Intel chips have 3MB cache/core whereas the Turions only have 512KB/core.
-RAM is huge now too. Prime example here would be Windows Vista (Home Premium and above especially). Running on 1GB of RAM, even with a good CPU, it can be a total DOG. Upgrade to 2GB+ and it runs quite nicely actually.
-Also, generally, but not always, a higher clock speed equals more heat output from the CPU.
