The cell goes through a time of growth between cell divisions and this is called

In a cell cycle, the time where the cell doesn't undergo cell division is called the interphase.
Its like a resting stage of the cycle.
During this period of time, the chromosomes (thread like structure of DNA) is rather unclear and cannot be seen, but at the same time the chromatins duplicate and double its number for cell division. This process is same for both mitosis and meiosis.