In evolutionary biology convergence is when we find two organisms that are not closely related phylogenetically with the same morphology or behavior. One of my favorite examples are icthyosaurs and dolphins. Ichthyosaurs were marine reptiles that lived about the time of the dinosaurs. Here's an image: http://www.google.com/imgres?imgurl=http://www.sedgwickmuseum.org/education/downloads/ichthyosaur.jpg&imgrefurl=http://www.sedgwickmuseum.org/education/gallery.html&h=864&w=1772&sz=220&tbnid=xx1gNAc8VpX3gM:&tbnh=73&tbnw=150&prev=/images%3Fq%3Dichthyosaur&zoom=1&q=ichthyosaur&hl=en&usg=__i4eg6bdQuh8Eq1nGf0n3zTqQyP0=&sa=X&ei=xcIsTY_9LYSs8AbaopGRCQ&ved=0CEQQ9QEwBg
They looked quite a bit like dolphins, or they did as far as we can tell from the fossil record. The reason why? They occupied the same niche, or the same role in the ecosystem. They were fairly large marine predators that ate primarily fish. So the needs and selection pressures that applied to icthyosaurs were more or less the same as they were for dolphins. Same selection pressures, same shape more or less.
So the weird thing about cephalopds is that there are three major ways that they are convergent with us, and vertebrates in general. The first is a closed circulatory system. They have a system of hearts and closed blood vessels. Most invertebrates just have an open body cavity and the oxygen carrying fluid just sort of washes around inside the animal. This change to a closed system may not seem like much but it is much more efficient and has allowed for the evolution of the second convergent feature.
Cephalopods are the most intelligent of invertebrates and likewise they have the largest brain compared to body size. This would not have been possible without the efficiency of a closed circulatory system. And not only does their brain contain a whole lot more neurons than most other invertebrates, it is also arranged into function specific "lobes" just like our brains. (Quick tangent: each of an octopus's arms has its own neurology such that an arm can be doing something productive without the octopus's brain knowing about it. Imagine your hands making a PB+J until suddenly you look down, delighted. Sandwich time! says the brain.)
The final and most complex form of convergence found in cephalopods are their eyes. Vertebrates have extremely complex eyes that allow us to do really cool things like focusing. We probably all take it for granted but most invertebrates see the world only in a blur of grays. For them detecting motion is far more important than what the actual object looks like close up so the need to focus has never really come up. For reasons that are still debated (oh, you scientists, constantly debating) there were selection pressures on cephalopods for them to develop a more complex "camera" eye. Most cephalopods still cannot see color but they have very good vision both close range and long distance. And they are able to focus to work out finer details than most invertebrates.
So the next time someone asks you (and I know they will) why cephalopods are so cool you can confidently answer: cephalopods are just like us! They have a closed circulatory system! How neat is that!?
And, as always, my neurons. Thank you, neurons!