When something senesces, it gets old and starts to show its age.
Senescing is a natural process, like when leaves turn brown and fall off the trees in the autumn.
Examples:
The fruit senesces and becomes soft and brown.
The old dog senesces and moves more slowly.
As the flower senesces, its petals wilt and fall off.
My toy senesces and starts to look old and worn out.
The building senesces and starts to crumble and decay.
The tree senesces and its leaves change color and fall off.