In complete block design, every treatment is allocated to every block. In other words, every combination of treatments and conditions (blocks) is tested.
For example, an agricultural experiment is aimed at finding the effect of 3 fertilizers (A,B,C) for 5 types of soil (1…5). There are 15 plots at the disposal of the researcher – 3 plots for each type of soil. Here fertilizers (A,B,C) are “treatments”, types of soil (1…5) are “blocks”; the “design” is the chosen distribution of the 3 fertilizers over the 15 available plots. In a complete block design, every possible combination of fertilizer and soil-type is used at least once.