Azulejo is not blue
It seems easy to make the connection in Portuguese azul (blue) to azulejo as the main color of the famous painted tiles are blue, but the origin cames from another word, az-zullayj, which means small polished stone and not from lāzaward that means blue.
The origin is from egypt and was introduced in the Iberian Peninsula by the Arabs, during the Sec. XIII. Primarily, they were mosaics cut from pliers, from a larger piece of glazed clay in one color.
Now Azulejo means a ceramic thin plate, usually square, glazed on one side, with varying designs and colors, used to coat surfaces. It is is one of the strongest expressions of Culture in Portugal and one of the most original contributions of the Portuguese genius to the Universal Culture.
Azulejo largely went beyond mere utilitarian function or its destiny of Ornamental Art and reached the transcendent status of Art as a poetic intervention in the creation of architectures and cities. The Azulejo art "painted" cities during centuries.
Back to the blue of azulejos the influence is oriental and comes from the chinese Porcelain after the Portuguese discoveries, centuries after the first azulejos are made.