Transgenic means that one or more DNA sequences from another species have been introduced by artificial means. Animals usually are made transgenic by having a small sequence of foreign DNA injected into a fertilized egg or developing embryo. Transgenic plants can be made by introducing foreign DNA into a variety of different tissues.
A transgenic animal is where you take a piece of DNA that's not normally found in that animal and place it back among its normal chromosomes. So for example, you can make a transgenic by having a piece of DNA that you clone in a laboratory and inject it into a fertilized egg of a mouse embryo, for example, then that becomes integrated into the chromosome. And then when that mouse is born, it can transmit that extra piece of DNA to its offspring. Transgenic animals can be used to model human diseases. So for example, if there was a particular human disease that results from having a mutated protein overexpressed, you can make a transgenic animal that also makes that same mutated protein overexpressed. This then provides us with a mouse model that then mimics that human disease that we can go into and actually study how that overexpressed mutant protein causes the disease, and we can also use that animal to test therapeutic interventions.