The word Transpose, as per Oxford Dictionaries, means 'Cause two or more things to exchange places' or 'Transfer to a different place or context'. Transposition of shares means change of order in which names of joint holders appear in a share certificate or in a demat account.
Example: If Mr. Harry and Ms. Emma are holding 10 shares in Qwert Pvt Ltd, and in their share certificate Mr. Harry's name is mentioned first and Ms. Emma's name is mentioned after it, then Mr. Harry is called the first holder and Ms. Emma is called the second or joint holder. If they want to change this order and make Ms. Emma the first holder and Mr. Harry the second holder, they have to request the company or their Registrar & Share Transfer Agent (RTA) or the stock trading company where the demat account is held.
How to apply?: It would be advisable that you contact the company/ RTA/ stock trading company to find out the documents required for this. If they accept requests only in specific format, then you can ask them to mail you the specific forms. You can find their address, to where all the documents have to be sent, on their official website.
You may write a letter with all the necessary details, enclose the required documents along with it and send it to the company for this purpose.