"Doubling" means playing exactly the same part as another instrument's part. Could be at an octave higher or lower or loco (unison) depending on the instrument itself.
"Doubling a flute melody with a piccolo" means the piccolo is playing exactly what the flute is playing but at an octave higher.
"Double the cellos" with, for example, double bass means the double bass is playing exactly what the cellos are playing but at an octave lower.
"Double the cellos" with, for example, bassoon means the bassoon is playing exactly what the cellos are playing at loco pitch.
Brass instruments usually double viola or cello's parts to strengthen the inner harmony.
In orchestration, doubling is usually used to:
1. strengthen an important part in terms of harmony
2. strengthen a part played by an instrument that is too weak to penetrate the full orchestra
3. create interesting timbre when 2 or more instruments play the same part at loco (eg; flute and oboe usually double each other)