"dog" is the singular form of a countable noun, and "dogs" is the plural form of the same noun. "Air" is uncountable-- you can't say "one air, two airs". In addition to counting, we will say "a" in front of singular countable nouns, but not in front of uncountable nouns.
singular countable: I saw a tree.
uncountable: I saw water.
BAD: I saw tree.
BAD: I saw a water.
Sometimes a word will have several definitions, and the singular countable definition might be different from the uncountable definition.
experience (uncountable)= knowledge and skill in a particular area="Bob has a lot of computer experience. You should hire him to fix your computer."
experience (countable)= a thing that happens="I had a lot of strange experiences yesterday. I saw a man with a banana on top of his head, and I saw a camel walking in the middle of the road."
Sometimes, there will be two different countable definitions of a word, and one of them will usually be used less often as a plural than another one.
pace (countable)= a step= "he walked three paces"
pace (countable, usually singular)=speed="He walked at a slow pace."
wood (uncountable)= a building material= "This house is made from wood."
wood (countable)= a type of golf club="Bob selected a wood instead of an iron."
the woods (countable, always plural)=a forest="The woods were dark and scary."
Other times, some words will always be in the plural or singular form.
For instance, in America, "math" is always singular, and in Britain, "maths" is always plural.
"accounts receivable" is always plural. It is the name of a single department, but it is grammatically plural, and since we use the plural form to talk about a single thing, we will never use the singular form.
the metaphorical meaning of "the negotiating table" is always singular.