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Hermitian Matrix is a special type of matrix, which is same as its conjugate transpose as expressed below.
In orther words, a Hermitian Matrix has following properties
One example of Hermintian Matrix is as follows. In this example, if you conjugate the matrix A and then transpose it, the result is same as the original matrix (A). So you can say the matrix 'A' is a Hermitian matrix.
One of the important characteristics of Hermitian Matrix is that Eigenvalues of all Hermitian Matrix are all real as shown in the following example.
For more practical meaning of Hermitian matrix, refer to Visualizing Hermitian Matrix as An Ellipse with Dr. Geo (I strongly recommend you to read this)
Related Reading : Hermitian Conjugate, Conjugate Transpose