ASN.1 has a number of different string data types. They differ in the range of characters they can support, and in how many octets are used to represent each character.
The string data type you will see mentioned most often is the UTF8String. This is the best data type for internationalization. UTF8 stands for UCS Transformation Format, 8-bit (where UCS stands for Universal Character Set). It in fact uses a variable-length encoding. The original ASCII characters have exactly the same encoding as in ASCII itself, using 7-bits, and with the top bit set to zero. All other characters have the top bit set to 1. Because the encoding is variable length, all known characters can be represented.