The most accurate reply is, “well, it’s complicated.”
There are a bunch of potential ways to define a species, but each fails in some manner or another. As a result there are a lot of potential ways to define species.
An example of the way a definition of species may fails is to look at the most commonly taught one, the Biological Species Concept, which basically states that if individuals can produce fertile offspring together then both belong to the same species. Well, this definition fails when it comes to asexually reproducing organisms, and there are too many exceptions to it. For example llamas and camels are clearly different (although related) species, no-one would claim them to be the same species, but they can produce fertile offspring (assisted fertilization, male camel, female llama). Macaques frequently hybridize producing fertile offspring, both anthropogenically and naturally at the margins of their species ranges, with rhesus/pig-tailed macaque and rhesus/long-tailed macaque hybryds being especially common. This sort of thing has increasingly been found to be the case in animals and is far more common in plants. As a result of these exceptions and problems, despite the prevalence of this definition being taught in school and in undergrad it’s not really used all that much in professional circles any more.
Here are a couple of incomplete lists of some of the ways species are presently defined:
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A brief overview of 26 different ways to define a species - not paywalled
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Zachos 2016 An Annotated List of Species Concepts - paywalled