Natural SELECTION is the process whereby certain traits give an organism a selective advantage in a particular environment. If the organism survives and subsequently reproduces, it is deemed to be "fit" when it produces offspring, which hopefully have those same traits. Variations occur in populations due to genetic variability, sexual reproduction, recombination and mutations. Ecological succession is the replacement of one community by another over time, resulting in a climax community. This community remains unchanged unless a disaster like fire, flood, etc. disrupts the climax community. Then, secondary succession occurs and the process will repeat. An example is bare rock after a volcano forms new land. This will eventually have moss and lichens growing on it. They will cause the rocks to weather and form soil. As soil building continues, grasses will be able to grow. They will attract new organisms to the area as they provide food and shade and can hold water in the soil. These will be replaced by shrubs, then pines, and eventually, oaks, beech and maples. The last two are the climax community. A beech-maple forest would have squirrels, birds, deer, chipmunks, etc and this community will continue in balance unless an ecological disaster occurs.
Natural selection is what occurs within a species when a member of that species has a physical trait that endows that member better equipped to survive as a member of that species. The idea is that member will pass that trait along to its offspring, and the members who are better equipped with these superior traits will be naturally selected, as the members without them will not survive, for one reason or another.
Ecological succession is what happens to a certain ecological setting after a disruption of what the setting was initially. A good example of this is what happens to a forest that had a wildfire go through it. Within two years, a new carpet of green replaces the remains of the burned forest floor. My grandfather had a field he planted peas in when I was a child, commonly referred to as "the pea patch". After my grandfather passed away, no one tended to the field anymore, and it was taken back by the pine tree forest that surrounded it.