An orchestra, at least in Western culture, usually has a fairly specific selection of instruments from which the orchestra is comprised ("orchestral instruments"). In contrast, an ensemble can be any collection of instruments, voices, dancers. An orchestra is always an ensemble, but not all ensembles are orchestras.
The specific instruments 'required' in an orchestra changed over time. In the Baroque period, it was common to have a string section (violins, violas, celli, basses), a couple of wind instruments (oboes, horns were common) and perhaps even a harpsichord. This changed through the Classical period, and by the Romantic period there were vast swathes of brass and woodwind instruments and a much larger string section. There was also more variety in percussion instruments.
A "wind orchestra" is an orchestra entirely comprised of wind instruments; a "chamber orchestra" is a smaller version of an orchestra but generally comprising of similar instruments to a full-size orchestra, except where impractical or unbalancing in terms of volume.
An orchestra will refer to a specific set of instruments, as Beth mentioned. There is usually a qualifying descriptor in front of it. A symphony orchestra refers to the group we normally associate with classical symphonies and tone poems. There are non-classical orchestras, too, like Big Band Orchestras and Gamelan Orchestras. Both refer to specific sets of instruments that play those kinds of music.
To the best of my knowledge, no vocal ensemble has ever been called an orchestra (pleading for experts to correct me here :-) ). Similarly, it's common for a combined performance to be "orchestra and chorus" rather than just "orchestra," so while "vocal ensemble" is a common term, as well as "instrumental ensemble," I think 'orchestra' is pretty much limited to instrumental groups.
We (sort of) know what a Symphony Orchestra is. Apart from that, as previous answers have demonstrated, the term is pretty much up for grabs. We might be fairly confident in saying that (unless used ironically) 'Orchestra' implies a sizeable group of players. But not necessarily THAT big.
'Ensemble' is an even looser term.