Final answer:
The cells Anton van Leeuwenhoek likely observed with his microscope and referred to as 'animalcules' due to their ability to move independently were probably protozoa or similar motile single-celled organisms.
Step-by-step explanation:
Anton van Leeuwenhoek is known as one of the first microscopists and the father of microbiology. Using his handmade lenses, Leeuwenhoek observed single-celled organisms that could move independently. The term 'animalcules' was used by him to describe these microscopic life forms because of their motility, suggesting that they were tiny animals. Given the characteristic of independent movement mentioned in the question, the cells Leeuwenhoek likely observed were probably protozoa or other types of motile single-celled organisms such as sperm. These observations contributed significantly to the development of the Cell Theory, which is foundational to understanding biology today.