Microorganisms are extremely small life forms, so small in fact that we cannot even see them with our naked eyes. Micro refers to one millionth part of a meter and these organisms are about that size (couple of order of magnitudes smaller or larger as well). Microorganisms include bacteria, protozoa, viruses, fungi, etc. We typically use microscopes to take a look at them.
Microorganisms evolved billions of years ago on Earth and are precursors to higher life forms like us. Microorganisms are both beneficial and harmful to us. There are a number of bacteria, such as lactobacillus (which help in formation of yogurt or curd) that are useful to our life. Similarly, there are a number of microorganisms such as (strains of) E. coli that are pathogenic (cause diseases) to us. We can also engineer microorganisms to behave in a certain fashion and use them for production of chemicals or cleanup of organic matter from wastewater.