In the Design of Experiments it is usual to carry out several tests at each treatment, this allows the amount of variation (experimental error) to be estimated. If each treatment is tested four times then there are four replications of the design, as long as the important requirement that the order of the runs is randomized is satisfied.
The purpose of randomization is to remove systematic error. If the runs are not randomized but each treatment is repeated several times before moving on to the next, then that is referred to as a 'repeat' or 'repetition' rather than a 'replication'.
If the runs are not randomized the ANOVA analysis should not be carried out using the repeats as individual readings. Instead the mean of the repeats should be treated as a single reading