The program, which uses a series of interactive virtual reality animations to mimic the movement of various fabrics, was devised by Nicola Davison ...
'The program is also designed to make shopping online fun and rewarding rather than just clicking through pages ...'
'Program' in the above examples refers to a computer program. It means a set of instructions used by a computer in order to perform a particular operation. Note that the British and American spellings are the same.
However, 'programme' refers to:
(1) a television or radio broadcast, such as a film or documentary;
(2) a sequence of planned activities, or a detailed plan of actions or events that are to take place;
(3) an information booklet containing details of a performance, such as a concert or a play.
Note that in American English, the spelling 'program' is used for the above meanings.