Why is it that the volcanoes found in the Tharsis Montes region near the Martian equator, (one of which is Olympus Mons) so much larger than those found on Earth. In comparison, Hawaii's Mauna Loa, the tallest volcano on Earth, only rises 10 km above the sea floor. Olympus Mons rises three times higher than Earth's highest mountain peak, Mount Everest. What makes these volcanoes rise to such enormous heights in Mars, when comparing to those found on Earth and the rest of the Solar System?
This is mostly due to the fact that Mars does not have plate tectonics. Therefore the plate stays above the hotspot without moving, allowing magma to rise and pile up at the same place for millions and millions of years. Above the Hawaii hotspot, the oceanic plate is moving, so volcanism tends to drift away with time (actually the volcanism happens at the exact same place from a mantle point a view, but its surface expression moves with the plate). It's why rocks of the Hawaiian-Emperor seamount chain are older in the West and younger in the East. This is true even at the scale of Hawaii island itself, where Kohala and Mauna Kea are extinct, while volcanism$-$or rather the plate$-$has shifted to Mauna Loa, Kīlauea and Lōʻihi.
Imagine if all the magma comprising these islands had piled up at the same place, it could have built a gigantic volcano like Olympus Mons! Well... not really. There is another parameter to account for: a theoretical limit to how high a mountain can possibly get, because of compressive strength of rock (or glacial erosion in some theories). See for instance answers in these questions:
- How high can a mountain possibly get?
- Why is Mauna Kea taller than the maximum height possible on Earth?
On Earth the limit is ~10 km. So even if magma kept piling up at the same place, the resulting mountain would start to laterally spread or collapse. But on Mars gravitational acceleration is lower, making the limit much higher.
The other answer is already pretty good: No plate tectonics and no water erosion allows material to pile up in one place, and then stay put. Neither is the case on earth: The plate moves away from the hot spot, transporting built up rocks with it and causing the magma to find another outlet a few miles over. Hawaii also tends to be a place where you can see water erosion happen in a pretty spectacular way.
There is one other reason, though: Earth's tectonic plates are not very thick -- oceanic plates, for example, are only 10-20 km thick. They bend down even just under an ice sheet like during the ice ages (or in Antarctica today). This process is called "isostatic adjustment", and you can think of it as the plate just sinking down into the region below that consists of a (somewhat) liquid state of rock which just moves to the side. It's a bit like when you step onto an ice flow: it just sinks down a bit. If this already happens with an ice sheet 1000 meters thick, imagine what would happen if you piled 30 km of rocks on top of a plate: it would just keep sinking down. In essence, every time you'd erupt some more lava and put it on top, the plate along with the base of the mountain would sink down a bit further. Mountains don't tend to build up very high in this process.
Why is this not happening on Mars? Because Mars is relatively small, and its interior has long cooled down to a degree where the crust (the solid part of the earth that on Earth consists of the tectonic plates) is vastly thicker: Many 100s of km thick, possibly all the way down to the core-mantle boundary. A result of this is that they can support vastly larger loads without crumbling or sinking into the more liquid layer beneath. As a result, they crust on Mars can support mountains that the plates on Earth could not.