Muy and Tan are adverbs of degree, also known as intensifiers
Think about them in their English equivalents:
Muy = Very (Used before an adjective)
"Él es un hombre muy fuerte" --> "He is a very strong man"
"Ella está muy enojada" --> "She is very angry"
"Sus padres deben estar muy orgullosos de él" --> "His parents must be very proud of him"
Tan = As, So, Such (Used for comparisons of equality, comparing qualities, emphasis)
"Mark es tan alto como su hermano" --> "Mark is as tall as his brother"
"Mi café está tan caliente que no me lo puedo tomar" --> "My coffee is so hot that I can't drink it"
"Este material es de tan buena calidad que no se puede romper" --> "This material is of such good quality that it cannot be broken"
Tan is also used in sentences like these:
"¡Qué día tan hermoso!" --> "What a beautiful day!"
"¡Qué coche tan caro!" --> "What an expensive car!"
Hope this helps you understand a little better. Good luck