In modern usage, philharmonic is usually a noun, meaning a symphony orchestra. This is a shortening of the once-common phrase "philharmonic symphony"; given that 'philharmonic' means 'loving music' and 'symphony' means 'sounding good', this borders on tautologous. This redundancy comes from a combination of wanting to sound grandiose, and the use of alternate terms to distinguish between various different large, fancy orchestras in the same city.
It appears that the use of philharmonic to refer to orchestras was popularized by the success of the Royal Philharmonic Society, a British music society formed in 1813. When the first big orchestra in the US was founded in New York in 1842, they went with the double-barreled Philharmonic-Symphony Society of New York (now commonly called the New York Philharmonic); the more restrained Austrians also founded the Vienna Philharmonic (Wiener Philharmoniker) in 1842, and these two set the tone for naming impressive orchestras across Europe and America.
These days, a philharmonic orchestra is a synonym for a symphony orchestra, namely a full-size Western orchestra containing from 70 to 100+ players. A smaller orchestra may be called a chamber orchestra.