Niederländisch vs. holländisch
The German words niederländisch and holländisch both refer to Dutch, but they have subtle differences in usage and connotation.
Niederländisch
A2Niederländisch is the official and more precise term for the Dutch language and anything related to the Netherlands as a whole.
Ich lerne niederländisch an der Universität.
(I'm learning Dutch at the university.)
Die niederländische Flagge hat drei horizontale Streifen.
(The Dutch flag has three horizontal stripes.)
Holländisch
A2Holländisch is a colloquial term that technically refers to things from the regions of North and South Holland, but is often used informally to mean Dutch in general.
Sie spricht fließend holländisch.
(She speaks Dutch fluently.)
Holländischer Käse ist weltberühmt.
(Dutch cheese is world-famous.)
Summary
While both niederländisch and holländisch are used to refer to Dutch, niederländisch is the more formal and accurate term for the language and country as a whole. Holländisch is more colloquial and, strictly speaking, refers to the Holland regions, but is often used informally to mean Dutch in general. In formal contexts or when precision is important, niederländisch is preferred.