Takt time is the rhythm of customer demand: the available production time divided by customer demand in the same period. If 400 parts must be delivered in a shift with 480 available minutes, the takt is 1.2 minutes per part.
Takt is not a measure of how fast you can produce, but how fast you must: processes faster than takt create overproduction; processes slower than takt create backlogs. Balancing against takt reveals which stations really constrain.
Takt presupposes reasonably levelled demand (heijunka) — if demand swings wildly from day to day, the takt swings with it, and balancing becomes impossible.
In practice you rarely design to 100% of takt. Stoppages, changeovers and natural variation mean a line built exactly to takt never reaches it — so cycle time is typically set at 85-95% of takt, leaving the rest as buffer. Skip that, and the backlog appears in the very first week, leading to the false conclusion that staffing is too low.