Basically, ∆Ct is the difference in Ct values for your gene of interest and your housekeeping gene for a given sample. This is to essentially normalise the gene of interest to a gene which is not affected by your experiment.
Using the ∆∆ Ct formula to calculate gene expression.
To use the ∆∆ Ct method, you require Ct values for your gene of interest and your housekeeping gene for both the treated and untreated samples.
As answered by Alkarim, delta ct is the difference in ct values of ur gene of interest and your endogenous control grnerally GAPDH, b-Actin etc. Now delta delta ct is the difference between delta ct of treated sample and control sample. This value finally used to calculate fold change.
For gene expression studies it's needed to perform delta delta ct method and calculate the log-fold changes between the housekeeping gene and gene of interest..