A thermocycler is simple: it heats up and cools down in series of programmable cycles. The thing being heated and cooled is often a tube of DNA and reagents. The strands of DNA denature, or separate into individual strands, at a specific temperature and the reverse happens (annealing) at cooler temps. Imagine peeling apart a double strand of DNA creating two single strands. Now imagine making each single strand whole again by plugging in free-floating nucleotides. You'd now have two strands of DNA when you started with one. This is a simplified explanation of DNA amplification and is quite useful for taking a small sample of DNA and making lots of copies for analysis like sequencing.