How I understand it.
Mutations occur at some scale, small or large, often. 99% of mutations have no eefect on the animals in question. of the remaining 1% that do effect a very small fraction would be benificial within the context of environmental pressures. So a species might find itself in a grassless environment because of draught or weather changes, and a member with a slightly higher reach, due to some little tweak that caused it to be just a little taller than it's other members, would giev it an advantage in survival. If you look at any given population you will find variations in hieght, weight, stamina et all are very common. So the one member who was made taller by mutation, something that might under normal circumstances not matter that much, becomes the best fed and most healthy of the bunch. And the healthiest member of the opposite sex will be attracted to this one. Chances are the female is also taller and slightly better adapted. These two pass these traits on to one or two of their offspring, which continue the process until the adaptation to the envirnment is adequate for the whole group. At this point nature will not select the taller animals anymore because all the animals are now able to be healthy and reproduce, and the smaller members will not be left out.
Oversimplified, but this is the general idea, I believe.