Here we use low-temperature scanning tunneling microscopy and spectroscopy to reveal the roles of the narrow electronic band in two 1T-TaS_{2}-related materials (bulk 1T-TaS_{2} and 4H_{b}-TaS_{2}). 4H_{b}-TaS_{2} is a superconducting compound with alternating 1T-TaS_{2} and 1H-TaS_{2} layers, where the 1H-TaS_{2} layer has a weak charge density wave (CDW) pattern and reduces the CDW coupling between the adjacent 1T-TaS_{2} layers. In the 1T-TaS_{2} layer of 4H_{b}-TaS_{2}, we observe a narrow electronic band located near the Fermi level, and its spatial distribution is consistent with the tight-binding calculations for two-dimensional 1T-TaS_{2} layers. The weak electronic hybridization between the 1T-TaS_{2} and 1H-TaS_{2} layers in 4H_{b}-TaS_{2} shifts the narrow electronic band to be slightly above the Fermi level, which suppresses the electronic correlation-induced band splitting. In contrast, in bulk 1T-TaS_{2}, there is an interlayer CDW coupling-induced insulating gap. In comparison with the spatial distributions of the electronic states in bulk 1T-TaS_{2} and 4H_{b}-TaS_{2}, the insulating gap in bulk 1T-TaS_{2} results from the formation of a bonding band and an antibonding band due to the overlap of the narrow electronic bands in the dimerized 1T-TaS_{2} layers.