I've realized that some pilots turn the air conditioning units (also called 'packs') OFF during takeoff, like in this video:
Is there any operational reason for that?
The "packs" (or A/C on the aircraft) are powered by engine bleed air. When bleed air is extracted from the engines, less thrust can be produced. This may be a problem if the airplane is taking off at a high elevation airport or the departure path requires a certain climb gradient to clear obstacles. This action does create some discomfort in the cabin so it's usually not preferred unless required for the safety.
Some newer airplanes are manufactured with an "APU to pack" configuration - i.e. the pilots leave the APU running during takeoff, which provides bleed air to power the packs. The workload on the engines are now reduced.
Pilots will turn off the packs for takeoff if maximum engine performance is needed or if there is a need to prioritize a high demand bleed draw. The particulars of the situations calling for a packs-off takeoff is airframe specific.
In the EMB-145, normal takeoff was with the APU bleed powering the packs. The specific configuration calls for engine bleeds off, APU bleed on, cross-bleed valve open and packs on. This lets the APU be the sole source of bleed air and the packs the sole consumer of bleed air. This is a typical configuration, but assumes that the APU is operational and that anti-ice will not be needed.
If the APU is inoperative or anti-ice is called for, then the takeoff configuration becomes engine bleeds on, APU bleed off, cross-bleed off, packs off. This isolates the APU from the bleed system (but keeps it available as a 5th generator) and makes the engines the bleed sources with no draw from the packs. This configuration with the APU inop allows the engines to avoid a performance hit from the bleed air taps (drawing compressed air at the 9th and 14 compressor stages of this particular engine). For anti-ice takeoffs, this configuration provides the ability to provide anti-ice as the APU bleed source is not powerful enough for this on the EMB-145.
The particular pneumatic configuration details will vary by airframe, and as mentioned in comments to the other answers, some airplanes have limitations on bleed valves being closed (e.g. to keep a pneumatic powered hydraulic pump operational) and some do not.
In summary, the reason for a packs off takeoff is likely for takeoff performance or for high demand needs such as anti-ice.
Best answer that I can think of, without the exact engineering or design info, is that since the A/C packs are run with engine bleed air, if you need the extra thrust from the engines, you'd turn off the packs for that extra power for take off...
When I did my dispatcher certificate, we used the 727... and from my notes, you'd get a 1500 lbs increase in runway limit performance, with the Packs off.