The Quarians created the Geth as labour machines, something actually everyone is going to do... create machines to help you.
A single Geth(Software) is a quite rundamentary AI, but a group of Geth can link together and form a neural network, that makes them more effective, smarter.
Each Platform (Hardware, the robots you face) can house various numbers of Geth.
The Quarians underestimated the power of the Neural Network as the Geth began to questionign their very existence. The Quarians out of fear what they had created (AI Creation is forbidden in Citadel Space... hello EDI and SAM.....) tried to shut them down to contain the situation but it was too late.
The Geth acted out of self defence and drove the Quarians, violently away from Rannoch. They stopped the pursuit and even returned to their daily work for which they were created in the first place.
The Reapers however are a synthetic/organic contstruct of unkown sophistication.
The way they truly function is never revealed, but it is obvious that they are machines, that contain and preserve the DNA of the Race it was created from. As Javik stated, experience is a biological marker, the DNA might act as a form of memory. It is controlled by an AI, supposedly the Leader of the Race but this is a very shackled AI, as it follows it's directive to obey the Catalyst and harvest life blindly.
And the Reapers aren't getting better each cycle. Harbinger, the first Reaper was created out of the strongest Race known to date, the Leviathans. He is stronger and more powerful then any other Reaper as far as we know.
