Theory:

Biological or organic evolutionoccurred due to the series of changes in the characteristics of groups of organisms throughout generations.
Biological evolution can be classified into two types:
  • Convergent evolution
  • Divergent evolution
Convergent evolution:
  
It is a type of evolution in which different species evolve similarities in their characteristics and functions due to the adaptation to a particular environment.
 
Divergent evolution:
  
It is a process in which the ancestral species diverges into multiple different species, ultimately giving rise to new species due to the accumulation of differences between the groups.
Important!
Adaptive radiation:
  
It is the diversification of a species into different forms to adapt to different environmental conditions for their survival.
This evolution can be better understood by observing the interrelationships between living animals and comparing parallels to extinct organisms. Evidence from other disciplines of biology also supports the interrelationship of the creatures.
These facts back up that all species have descended from a common ancestor.
The three major evidences that prove biological evolution are as follows:
  1. Evidences from comparative anatomy
  2. Evidences from embryology
  3. Evidences from palaeontology
1. Evidences from comparative anatomy
These pieces of evidence include comparing anatomical and morphological characters and thereby prove that they possess a common set of characteristics.

Based on the structural and functional similarities and variations, these are studied under various categories as follows:
  • Homologous organs
  • Analogous organs
  • Vestigial organs
  • Atavism
1. Homologous organs:
The organs from various animals or plants with a similar structure, identical developmental origin, and diverse functions are known as homologous organs.
These organs of different organisms may have similar basic anatomical structures as they are inherited from a common ancestor with similar developmental patterns in embryos. However, they have different morphological features and functions.
 
How do we find common traits while trying to follow evolutionary relationships? Because they are acquired from a common ancestor, these features in different creatures would be comparable.
Example:
Consider that mammals, like birds, reptiles, and amphibians, have four limbs.
As previously stated, these organs must have evolved from a common ancestor that evolved into organs with various anatomical traits that were appropriate to their distinct habitats.

Such types of organs are known as homologous organs, and the term homology refers to common ancestry. This type of evolution among organisms is known as divergent evolution.
Example:
800px-Homology_vertebrates-en.svg.png
Homologous organs
 
Mammalian forelimbs are homologous structures. A human hand, a cat's front leg, a whale's flipper, and a bat's wing all have diverse shapes and functions. Their growth patterns and basic bone structure are identical.
 
Thorns and tendrils of some plants are other example (different appearance and different functions). Thorns are modified leaves on plants like Bougainvillea. They serve as a type of protection. Cucurbita or cucumber tendrils are also modified leaves. Climbing is one of their functions.
Reference:
https://en.wikipedia.org/wiki/Homology_(biology)#/media/File:Homology_vertebrates-en.svg