Particles are perhaps the most frustrating part of Japanese grammar for most English speakers. Most English speakers learning Japanese are aware of verb tenses and conjugations, so the variety of them in Japanese does not seem to surprise the learner. But particles are quite foreign to most English speakers, confusing them to no end.
English uses prepositions to modify nouns and verbs. Prepositions such as "to", "at", "by", "around", and "without" should be familiar to anyone forced to learn the rudiments of English grammar in their school days. Prepositions are members of a class of linguistic objects called adpositions. The opposite of prepositions, postpositions are usually found in languages which lack prepositions. In some languages such as Finnish these postpositions have become glued to the words they modify, over time resulting in a set of fixed declensions for nouns and conjugations for verbs. Indeed, some linguists theorize that all nominal declensions (and verbal conjugations) derive ultimately from postpositions being suffixed to the words they modify. Following this theory, a language which fossilizes its postpositions into nominal declensions (a.k.a. cases) eventually ends up needing a replacement set of adpositions and so, perversely, produces prepositions to fill the gap.
Japanese has not gone so far as to completely fix its postpositions into nominal declensions and verbal conjugations. Instead its postpositions function as particles, small word-like units which modify the meanings of the phrases to which they are attached. Particles do not function as independent word units, they lack any meaning of their own. Thus, a sentence like "が" cannot possibly have any sort of meaning, either explicit or implied. It might be used as a prompt, one speaker saying the particle to prompt another speaker to finish their statement. But no meaning can be applied to the particle itself in any context.
Particles used as prompts are actually fairly common. The particle で is derived from the copula verb だ and is used to connect sentences together. It works somewhat like English's 'and' or 'so'. This particle is often heard alone when a listener is prompting a speaker to finish a sentence which they have left incomplete.
がっこう に いって
"I went to school and..."
で、すずき くん を みた
"And I saw Suzuki."
Other than this sort of usage particles are typically not used alone.
There is a very fine line between particles and verb (or adjective) conjugations in Japanese. Oftentimes a conjugation will seem to be just that until suddenly you notice that it is also attached to a noun in some random exceptional situation. Or that a particle for some strange reason seems to be only attachable to verbs and won't mate with anything else. This is probably because modern Japanese is in the midst of a change of emphasis from particles to conjugations, or vice versa. Linguistic speculation has not provided any conclusive answer yet. But suffice to say that you should expect particles and verb conjugations to regularly blur the boundaries between parts of speech.