Specifically, Holy Cross is used to refer to the True Cross on which Jesus was crucified.
In general, Holy Cross distinguishes the cross as religious and not simply a decoration. For anything 'holy', the religion does not have to be Christian - the Qur'an and Torah are holy books and we all enjoy our holydays.
The origin of the word 'holy' is obscure: it could have evolved from the Old English hālig, which means 'wholeness' (where the first 'e' is pronounced 'i'). Alternatively, it may be derived from Old High German hulis, meaning 'holly'. The holly tree was considered a sacred plant in both pre-Christian Celtic and Roman religions.
Today, something that is holy means it is recognized as sacred, godly, saintly, and spiritually pure.