Theory:

The generation of genetically modified (GM) plants and animals is one of the most significant advances in genetic engineering.
Genetic modification refers to altering or manipulating genes in an organism using rDNA techniques to produce the desired characteristics.
The DNA fragment (containing foreign genes) inserted is called a transgene.
Plants or animals expressing a modified endogenous gene or a foreign gene are also known as transgenic organisms.
The plants or animals in which foreign genes have been introduced through genetic engineering are transgenic plants or transgenic animals. They are also known as Genetically modified organisms.
 
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Transgenic zebra fish larva shows the blood vessels
 
Transgenic plants are more stable, have better nutritional content, are disease resistant, and can tolerate a various environmental conditions. Similarly, transgenic animals are employed to manufacture low-cost therapeutic proteins and increases livestock quality. The table below lists some examples of genetically modified plants and animals:
 
Transgenic plants:
 
Objective
Gene inserted
Achievement
Improved nutritional quality in RiceBeta carotene gene (In humans, Beta carotene is needed for the synthesis of Vitamin A
Golden Rice (Genetically modified rice can produce beta carotene, that prevents Vitamin A deficiency)
Increased crop productionBt gene from bacteria Bacillus thuringiensis. (Bt gene produces a protein that is toxic to insects)Insect resistant plants (These plants can produce the toxin protein that kills the insects which attack them)
 
Transgenic animals:
 
Objective
Gene inserted
Achievement
Improved wool quality and productionGenes for synthesis of amino acid, cysteineTransgenic sheep (gene expressed)
Increased growth in fishesSalmon or Rainbow trout or Tilapiagrowth hormone geneTransgenic fish (gene expressed)
Golden Rice: An example of a transgenic plant:
It is a transgenic variety of rice (Oryza sativa) that contains good quantities of Beta carotene, a principal source of Vitamin A. Since the seeds or the grains are yellow, the rice is called golden rice. Professor Ingo Potrukus and Peter Beyer produced genetically engineered rice by introducing three genes associated with the synthesis of carotene
 
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Normal rice vs Golden rice
  
Other examples of transgenic plants: Bt Cotton:
  
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Bt cotton
Transgenic Salmon: An example of a transgenic animal:
Genetically modified salmon was the first transgenic animal for food production. The genetically modified sperms were fused with normal eggs or ova of the same species.
 
The zygotes that grew into embryos produced larger adults than either of their parents. Transgenic salmon have an additional gene that codes for growth hormone, growing significantly larger than non-transgenic salmon.  
 
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Transgenic Salmon
 
Other examples of transgenic animals: Transgenic sheep:
  
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Transgenic sheep in the left vs normal sheep in the right
Reference:
https://commons.wikimedia.org/wiki/File:Golden_Rice.jpg
https://commons.wikimedia.org/wiki/File:Pic-bt-cotton-punjab-farmer.jpg
https://commons.wikimedia.org/wiki/File:Salmon4.jpg
https://commons.wikimedia.org/wiki/File:CSIRO_ScienceImage_1953_Difference_Between_Transgenic_Sheep_and_Normal.jpg
https://www.flickr.com/photos/nichd/43894416685