Within biology, the term is used in at least two distinct ways. The more common usage (and the first one I encountered in my studies) describes a large, diverse group of photosynthetic organisms that are capable of acquiring energy from sunlight (autotrophy) and from the degradation of preformed organic compounds (heterotrophy). This definition from the Smithsonian Environmental Research Center gives an idea of how broadly the term is applied.
Mixotrophic organisms gain their nutrition through a combination of photosynthesis and uptake of dissolved or particulate organic material. However, they vary widely in their photosynthetic and heterotrophic capabilities. Some mixotrophs are mainly photosynthetic and only occasionally use an organic energy source. Others meet most of their nutritional demand by phagotrophy, but may use some of the products of photosynthesis from sequestered prey chloroplasts.
The other usage is limited to prokaryotes* and is much more specific in its meaning. Here, mixotrophy refers to organisms that are capable of acquiring energy from the oxidation of inorganic compound but are unable to fix carbon. This means they must obtain organic carbon for biosynthesis. A relatively well know example of an organism in this group is Beggiatoa
*Yes I am going to continue using the term and, at the risk of contributing nothing of substance to the discussion, I will probably put up a post about it later in the week