Orchestration is the study or practice of writing music for an orchestra (or, more loosely, for any musical ensemble, such as a concert band) or of adapting music composed for another medium for an orchestra. Also called “instrumentation”, orchestration is the selection of different instruments to play the different parts (e.g., melody, bassline, etc.) of a musical work. For example, a work for solo piano could be adapted and orchestrated so that an orchestra could perform the piece. Only gradually over the course of music history did orchestration come to be regarded as a separate compositional art in itself. In classical music, most composers write the melodies, chord progression and musical form for a piece and, then, if they want the piece to be played by an orchestra, they orchestrate the piece themselves. In musical theatre, however, the composer typically writes the melodies and then hires a professional arranger or orchestrator to devise the parts for the pit orchestra to play.

As profession
An orchestrator is a trained musical professional who assigns instruments from an orchestra or other musical ensemble to a piece of music written by a composer, or who adapts music composed for another medium for an orchestra. Orchestrators may work for musical theatre productions, film production companies or recording studios. Some orchestrators teach at colleges, conservatories or universities.

In practice
The term orchestration in its specific sense refers to the way instruments are used to portray any musical aspect such as melody, harmony or rhythm. For example, a C major chord is made up of the notes C, E, and G. If the notes are held out the entire duration of a measure, the composer or orchestrator will have to decide what instrument(s) play this chord and in what register. Some instruments, including woodwinds and brass are monophonic and can only play one note of the chord at a time. However, in a full orchestra there are more than one of these instruments, so the composer may choose to outline the chord in its basic form with a group of clarinets or trumpets (with separate instruments each being given one of the three notes of the chord). Other instruments, including the strings, piano, harp, and pitched percussion are polyphonic and may play more than one note at a time. As such, if the composer/orchestrator wishes to have the strings play the C major chord, she could assign the low C to the cellos and basses, the G to the violas, and then a high E to the second violins and an E an octave higher to the first violins. If the composer/orchestrator wishes the chord to be played only by the first and second violins, she could give the second violins a low C and give the first violins a double stop of the notes G (an open string) and E.

Additionally in orchestration, notes may be placed into another register (such as transposed down for the basses), doubled (both in the same and different octaves), and altered with various levels of dynamics. The choice of instruments, registers, and dynamics affect the overall tone color. If the C major chord was orchestrated for the trumpets and trombones playing fortissimo in their upper registers, it would sound very bright; but if the same chord was orchestrated for the celli and string basses playing sul tasto, doubled by the bassoons and bass clarinet, it might sound heavy and dark.
Note that although the above example discussed orchestrating a chord, a melody or even a single note may be orchestrated in this fashion. Also note that in this specific sense of the word, orchestration is not necessarily limited to an orchestra, as a composer may orchestrate this same C major chord for, say, a woodwind quintet.

In the 20th and 21st century, contemporary composers began to incorporate electric and electronic instruments into the orchestra, such as the electric guitar played through a guitar amplifier, the electric bass played through a bass amplifier, the Theremin and the synthesizer. The addition of these new instruments gave composers new options for creating tonal “colours” in their orchestration. For example, in the late 20th century and onwards, a composer could have a melody played by the first violins doubled by a futuristic-sounding synthesizer to create an unusual effect.
Orchestral instrumentation is denoted by an abbreviated formulaic convention,[1] as follows: flute, oboe, clarinet, bassoon- horn, trumpet, trombone, tuba. More details can be contained in brackets. A dot separates one player from another, a slash indicates doubling. Timpani and percussion are denoted 2Tmp+ number of percussion.
For example, 3[1.2.3/pic] 2[1.Eh] 3[1.2.3/Ebcl/bcl] 3[1.2/cbn.cbn] tmp+2 is interpreted as:
3 flautists, the 3rd doubling on piccolo
2 oboists, the 2nd playing English horn throughout
3 clarinetists, the 3rd doubling also on E-flat clarinet and bass clarinet
3 bassoonists, the 2nd doubling on contrabassoon, the 3rd playing only contra
Timpani+ 2 percussion.
As an example, Mahler Symphony 2 is scored: 4[1/pic.2/pic.3/pic.4/pic] 4[1.2.3/Eh.4/Eh] 5[1.2.3/bcl.4/Ebcl2.Ebcl] 4[1.2.3.4/cbn]- 10 8 4 1- 2tmp+4-2 hp- org- str.

Source: Orchestration – Wikipedia