Semi-formal is a grouping of dress codes, indicating the sort of clothes worn to events with a level of formality between informal (i.e. lounge suit) and formal. Historically it was used as a daytime or eveningwear dress code, but will now be seen almost exclusively in the context of evening wear. In the day time (before six o'clock) it would have been a black tail-less coat with formal (striped or checked) trousers (this combination is called stroller in America). For evening wear, it is traditionally synonymous with black tie (tuxedo in American English), but the interpretation and description of dress codes in different social settings and continents now varies.
Terms like 'informal' or 'semi-formal' are used to describe a classification of dress, so would not often be directly given on an invitation; instead, the direction for the guest will normally be 'lounge suit' or 'black tie' (tuxedo) where appropriate, which removes some of the ambiguity.