There is no more capricious field of study than linguistics. This is primarily because its rule sets and tools have come about, more often than not, based on things (languages) that are constantly changing themselves. Just as you hear a new slang word on your bus ride to work, you forget about a word you grew up with that no longer falls into the vernacular. As you remember having your knuckles slapped by a ruler for ending a sentence with a preposition, you hear commentators on NPR doing just that.
That being said, speakers of any given language use a finite set of rules to produce and understand an infinite set of possible sentences. Those rules are part of the grammar of a language, which develops when you acquire the language sound system (the phonology), the structure of words (the morphology), how words may be combined into phrases and sentences (the syntax), the ways in which sound and meanings are related (the semantics), and the available words (the lexicon). All of this is considered linguistic competence. This writeup will focus on the concepts of lexical semantics, semantic properties, and phrasal/sentential semantics.
As Roman Jakobson said, "Language without meaning is meaningless."
Lexical Semantics
When learning a language, it is important for all speakers to agree upon meaning of certain strings of sounds and to learn how to combine these units into larger units that also convey a particular meaning. Anyone who has tried to learn French as a second language recognizes this difficulty (e.g. transferring the last sound of the first word onto the first sound of the second word under certain circumstances). Agreeing upon these rules means that we are not free to change the meanings of these words at will. If we did, language would not be useful at all.
Like a dictionary, the human brain hangs out on top your neck filled with words--thousands of them, quite literally. The knowledge of these words aids you in creating meaningful sentences and phrases and ushers communication through language. Even though it is common practice to use a word and then immediately think to yourself, "Wait a minute, what does that word really mean?" it is often the case that you've used it correctly without conscious effort. That is part of linguistic knowledge and is therefore part of the grammar of the language, burned into your brain at an early age.
Semantic Properties
All words and morphemes have meaning. If I were to say, "The rain caused Bixby's hair to flatten in an unseemly way," you access the dictionary in your brain to acknowledge that the water that falls from the sky turned some guy named Bixby's hair into something that was not what Bixby wanted. These bits of information, that the brain immediately cogitates, are parts of the semantic properties of the word on which the speakers of a language agree. The vast majority of words in a language are defined in similar ways.
These semantic properties can act as a part of the meaning of many words. For example, "male" is a semantic property that helps to define father, son, dad, stud, man, rooster, bull among others. The first three in the list are also distinguished by the semantic property "human," which is also found in construction worker, actor, artist, writer, astronaut, child, baby. The last two of these words are also distinguished by "young."
Phrasal / Sentential Semantics
Just as all words and morphemes have meaning, so too do all phrases and sentences. Phrasal/Sentential Semantics deals with this construct. As the dictionaries in our brains process words into sentences, we don't have to consciously think about how to form them into sentences, plumbing the depths of our linguistic competence automatically.
Just as a phrase, one that may be meaningless by itself such as "the thick book," our linguistic competence pulls from that phrase additional meaning. We pull the adjective thick out to apply directly to the noun book, and though we lack additional meaning (for example, a verb in this case), the phrase can make semantic sense all by itself. However, in the case of graded adjectives (such as "big" or "alleged"), the phrase must be further diagnosed in almost a mathematical way, leaning heavily on the noun meanings to make arguments.
Now, this has been but a small piece of the study of semantics. Additional fields of semantic study: Thematic roles, linguistic and non-linguistic context and Grice's maxims, which I have omitted because of the specific nature of each and large quantity of knowledge available to each. | 
