He is pictured on the side of a mountain with a gently sloping road leading to the summit. He tells us that evolution is like climbing this mountain - by taking one small step at a time, the summit can eventually be reached.
The driving concept behind evolutionary theory is "survival of the fittest". The idea here is that, if an organism is better suited to its environment than other organisms that are also present, then it will tend to survive, while the other (less fit) organisms will die out. Some evolutionists propose that mutations can produce changes in an organism that might give it a competitive advantage, and so it will better able to survive. In Dawkins words, it will have taken a step up "Mount Improbable".
This all sounds very plausible, except it ignores two major problems.
The first problem is that for this selection process to occur, a self reproducing organism needs to already exist. An organism that can feed itself and reproduce itself is already very complex. Producing a robot that could do this is certainly well beyond current human technology. No-one, including Dawkins, can tell us how this first organism came to exist, or what it looks like. Without this first self reproducing organism, we cannot even start to climb the mountain.
The second problem is that, in the real world, mountains don't normally have nice smooth roads leading directly to the summit.
If you imagine you are travelling towards your nearest mountain, you will most likely find that somewhere or other the road will actually go downwards before it goes up again. If you have the strategy of always going upwards, and never down, then you will be stuck at the first little hill, unable to go any higher.
In mathemetics this is called having a local maxima. When solving any problem, if one uses the strategy of always taking the steepest path leading upwards, one will eventually arrive at a summit, where it is impossible to go further up, as any further movement now leads down. In biological terms, any change will make the organism "less fit to survive". However, we have no way of knowing whether there might be another summit that is even higher, if we had taken a different path.
This is the problem with Dawkin's slow and sure climbing of Mount Improbable - survival of the fittest/ natural selection, will not allow you to go down in order to go up again. You will most likely be stuck at a little hillock, rather than the top of the mountain.
In practice, natural selection will actually take an erratic path, zig zagging all over the place as random changes occur - but it will always be moving upwards, moving downwards makes the organism less fit to survive - a competitive disadvantage - so the change will die out. A change that locally increases the survivability will be blindly followed no matter how far off it is to pointing towards the path to the highest mountain.
So, if you start out at sea level to climb Mt Everest by following this strategy, you will only end up climbing the first sand dune!
And of course, all of this assumes that you didn't actually start by meeting an unclimbable cliff.
Dawkins is certainly accurate when he terms it Mount Improbable - it is so improbable as to be impossible.