I understand that it's a method that ascribes purposes to things. I have heard people speak very highly and lowly of it. On the one hand people say it has greater explanatory power than cause and effect. On the other, it assumes purpose in a meaningless universe. So which is it? Is it a good framework?
"Teleology" is the idea that a system will inevitably end up in a certain state. The end state is defined in advance - from a distance (Greek: teleo, as in television, teleport etc.) - and any developments of the world before then will have no effect on the end state.
Christian dogma is 'teleological' for instance, because it states that eventually Jesus will return to Earth, return the dead Christians to life, and then everyone will live eternally in the kingdom of God. Its end state is completely defined, and no actions of humanity can affect whether or when Jesus' return will happen.
Hegel's dialectical idealism is also teleological, because he believed that each epoch of history is defined by certain internal contradictions that, when resolved, would lead to a new epoch - each epoch being "closer to God" until the perfect social system was reached (which he also thought had already happened, the literal perfect system of society in his view being constitutional monarchy).
Marx's dialectical materialism is often slandered as being teleological, because it states that capitalism will eventually be overthrown due to its internal contradictions, resulting in communism. Critics say things like, "it's utopianism", "it's just another kind of religious belief", etc. However, this is not just a philosophically idealist assertion of what will happen, it is a scientific prediction based on the observable development of capitalism. It is no more teleological to say that capitalism will give way to communism than it is to say that a fire will eventually burn to ash - a full understanding of the internal contradictions and laws governing each process means you can accurately predict the end state.
However, unlike a teleological framework, dialectical materialism also understands that those internal contradictions and their development can be overpowered by external conditions - the fire, which operating under its own laws must burn all its fuel to ash, could have a bucket of water dumped on it. The fire would go out without having turned the fuel to ash, but the original prediction based on its internal contradictions wasn't wrong, it was just superseded by external factors - just like Marx's original prediction, that communist revolutions would take place in the most developed capitalist countries, was thrown out by imperialism, which introduced a greater contradiction between imperializing countries and the peripheral nations they exploit. Lenin found that, due to the confounding factor of imperial plunder pacifying the workers of the imperial countries, communist revolutions would instead take place wherever the chain of imperialism was weakest - exactly as it was in Russia in 1917.
So tl;dr, teleological frameworks are incorrect, being philosophically "idealist" - suggesting that purely mental processes (originating in either human will or "the mind of God") determine the development of the world. Thankfully, the philosophy of the working class does not have this flaw, instead making predictions based on scientific analysis.
No, τέλος and τῆλε are different words.