The idea is that with period instruments you get a more faithful reproduction of the sound the composer imagined as he/she wrote the piece of music.1
There is some question as to whether or not this is actually the case, for
past performance is not necessarily indicative of future results. Rather, there is some question as to whether or not this is an
aesthetically valid line of
interpretation. These questions are referred to as issues of performance practice or, even more carefully, the practice of
historically informed performance.
It has been observed by examining pipe organs in Europe, that in the 17th Century standard pitch was inconsistent from town to town, and was much lower than it is today.2 In the performance of works from the Baroque in a period style it is customary to set pitches around A=428. A friend of mine who is a lutenist has tuned as low as A=415 for some concerts of early Baroque music.
Musical instruments are fragile objects. While violins (and a few celli) from celebrated makers3 have survived because of their innate sonorousness, nearly all of them have been rebuilt at one time or another, often to accommodate greater string tension and produce more sound at a higher pitch. Remarkably few wind instruments have survived. There are, however, treatises on the construction of instruments that have survived. The combination of treatises and examples by skilled craftsmen have reproduced many different types of instruments that have not been heard for a hundred years or more: the lira da brache, the violone, the harpsichord4, the theorbo, the oboe d'amore, the basset horn, and the viola da gamba. Even the viola d'amore, a favorite of the composer Paul Hindemith, had been (relatively) unheard for at least 50 years before he wrote his chamber concerto for it.
Musical style is the most insubstantial issue to discuss, as it concerns the way the players play their instruments. Take (or leave) vibrato, for instance. It has been thought that vibrato was not used in early Baroque music.5 Other style issues include ornamentation, staccato, and rubato.
As musical taste and scholarship change, the ideal of period performance has changed as well. We don't know what Felix Mendelssohn was thinking when he first conducted J.S. Bach's Saint Matthew Passion, but that was the start of our (modern) tradition of performing older music and the beginning of the recognition of issues of period performance. For my part, I strongly believe that there is no right or wrong regarding these issues. Every musical performance is an interpretation and de gustibus non est disputandum.
As an example, take Bach's Brandenburg Concerto, the one for flute, trumpet, oboe and violin. When Toscanini recorded this in the late 1940s, he placed an E-flat clarinet on the trumpet part, as Baroque trumpets (a valveless length of tubing, sounding an 8-foot C, and played on the overtones) were unavailable or unwanted. Critics asked why couldn't he have used a brass instrument (although what we now call the piccolo trumpet had not yet been developed). He defended himself by stating that in the score, Bach had writen "clarino", and the nearest cognate was "clarinet". This twisted use of one's own native language allowed the maestro to perpetrate what was, perhaps, an act of aesthetic violence. But his E-flat clarinetist was a damn sight better than any trumpeter.
1From a write-up by kamamer.
2Today A=440 Hz is considered standard pitch, however, the Chicago Symphony seems to be higher, around A=452Hz, it makes their horns and trumpets sound more bright while their string players fear for the effects of the increased tension. This was probably instituted by the conductor Fritz Reiner, and continued through the years under Sir Georg Solti. It is now regarded as a major component of what is referred to as "The Chicago Symphony Sound" in classical record reviews.
3For example, the Cremona masters: Antonio Stradivari, Nicolo Amati, and Guarnari.
4In the 1900-10s a piano builder in Poland designed a harpsichord based on a cast iron frame that had the expressive volume of the piano. It was fashionable at the time but ultimately died out. It has re-surfaced in some of Elliot Carter's works.
5There are dissertations I have not read that cover this subject and the corollary one of ornamentation.
SUGGESTED LISTENING ASSIGNMENT: Take a piece like the The Well Tempered Clavier and listen to every available recording you can get. Okay, compare just a few: Landowska (modern harpsichord, 1940s), Glenn Gould (piano, 1970s), and Bob van Asperen (clavichord, 1980s). Or find a whole mess of recordings of the Bach Cello Suites, like Pablo Casals (unrepentent romantic), Mstislav Rostropovich (modern romantic), Yo-yo Ma (modern, but tempered by ideas of period performance), and Jordi Savall (period performance), and compare. But most of all, LISTEN.