There are roughly 3 levels of specialization of computing equipment:
CPU (like in your laptop) is the most generic of them all. It can do everything, but this versatility comes at a price of slow speed and high power consumption. CPU is programmed on the go, the instructions come from RAM. Programs for CPU are quick, cheap and easy to write and very easy to change.
FPGA (which means Field Programmable Gate Array) is the middle tier. As it's name implies it can be programmed "in the field", that is outside of a factory. FPGA usually gets programmed once, this process can be described as setting up it's internal structure. After this process it behaves like a tiny computer specialized for the one task you've chosen for it. This is why it can fare better than generic CPU. Programming FPGA is very difficult and expensive and debugging them is very hard.
ASIC (which means Application Specific Integrated Circuit) is the ultimate specialist. It's a chip designed and produced for one and only one task - a task it does extremely fast and efficiently. There is no possibility to reprogram ASIC, it leaves the factory fully defined and is useless when it's job is no longer needed. Designing ASIC is something only large corporations can afford and debugging them is well, pretty much impossible.
If you think in "cores", then look at it this way: CPUs have 4, 6, maybe 8 big cores that can do everything. ASICS often have thousands of cores, but very tiny ones, capable of one thing only.
You can look at bitcoin mining community. They do SHA256 hashes.
- CPU core i7: 0.8-1.5 M hash/s
- FPGA: 5-300M hash/s
- ASIC: 12000M hash/s per one tiny chip, 2000000M (yep, that 2T)hash/s for one 160-chip device
Of course, those ASIC babies cost almost $2000 when mass produced, but it gives you an idea about how a jack-of-all-trades can fare against a specialist.
The only question is: can FPGA bring you more savings than designing it would cost?
Of course, instead of running it on ONE laptop, you can try running it on 20 PCS.