, we put spaces between our words, but we don't in speech
. Language is continuous, yet we feel it should be clearly divisible into segments. We call these segments "words", but in linguistics
the term has no precise meaning, because there are different ways of dividing up an utterance
Disregard the written or graphic words for now and consider other levels of linguistic structure.
Morphology studies the pieces of words that have a distinct function: in The children are playing there are six morphs, since -ren marks plural and -ing marks continuous. The morph -ren is one realization of a plural morpheme, which also includes the more usual -s, -es. Morphemes may be regarded as "morphological words".
Semantics studies meanings. In The children are playing only two morphemes, child and play, are fully meaningful. The other four are essentially grammatical. Play and playing are different forms of the same "semantic word": you wouldn't find playing listed separately in a dictionary. A semantic word is usually called a lexical item or a lexeme. They belong to open-ended classes like noun, adjective, or verb; whereas grammatical elements with very little semantic content, like the and -ing, belong to closed classes with few members.
A compound like chief inspector consists of two lexical items linked together, but the linkage may become tight enough that they can be regarded as a single lexical item, with its own place in the dictionary: head master, head-master, headmaster, or vacuum cleaner, or even magnetic resonance imaging. Semantically, each of these denotes a single thing.
Phonology studies how the sounds of the language are put together. In our example there are two stressed syllables, and the others are unstressed. Being unstressed doesn't imply an element isn't a word: we would call the a word because it can be greatly separated from children by other, stressed, words, as can are and playing: e.g. The very untidy children are still playing. But in another language, such as Arabic or Hebrew or Swedish or Romanian, the definite article is joined to the noun.
In French, we write je ne le vois pas 'I can't see it', but the three grammatical elements are not separate in pronunciation: phonologically, it's only two words jenelevois pas. Bantu languages have a very similar way of arranging morphemes on the front of verbs, but the custom in most of them is to write it all as one word. The French (and Bantu) morphemes are inseparable, unlike English the: you can't use je by itself. Elements like this, treated as words in some respects but not fully independent phonological words, are called clitics.
In Japanese the subject particle ga is pronounced [Na] (= nga). In romanization we write it as a separate word, but apart from this particle, the ng pronunciation of g only occurs inside words. So phonologically, this is a suffix rather than a word.
Syntax studies the arrangement of words (or rather morphemes) in the sentence. A "syntactic word" would therefore be something that holds together as a unit and can be moved around in larger structures. The English possessive marker 's is a fully independent word at the syntactic level, unlike case endings in most languages: if a man has a daughter, 's looks like a case ending in the man's daughter, but less so in the man in black's daughter or even the man I met in the pub last night's daughter.
Mostly, these concepts will overlap enough that we can continue to talk about words without specifying the level of description. In European languages the written word spacing is adequate. But in unfamiliar and unwritten languages, with no prior guide, there is no definite need to decide whether a morph is or is not a separate word: you just describe how it behaves at various levels.
The word, whatever kind it is, is a unit of structure of language. It is at an intermediate level, between utterances and their meanings and implications at one end of a scale, and phonetics and phonology on the other end. A word is typically something that has an idiosyncratic meaning, not predictable from its parts; though idioms also have that property, such as 'put up with' or 'kick the bucket', and compound words often have predictable meanings. It is only a level of structure: it is not an atom from which the rest of language is built up. Languages are not collections of words.