When you talk about "shrimp" in the plural, there's no "s." However, how can you explain it grammatically?
Some words may be either singular, plural, or uncountable, depending on how they are used in a particular context. That's just the way it is. There's really no grammatical explanation to it, although for some words, there may be historical explanations behind how their plurals are formed.
I should note, however, that "shrimp" is actually one of those words where the plural form may be "shrimp" or "shrimps", depending on the speaker's dialect.
shrimp (countable and uncountable, plural shrimp or shrimps)
In English we have mass nouns such as wood or rice. You cannot count a mass noun by putting a number in front of it (two books) or pluralize it by adding an -s (lamps). To indicate quantity you write the unit of measure in front of the mass noun. For example, you would write "two cords of wood" or "ten feet of wood" or "two pounds of rice".
It seems the grammatical reasons for this are obscure. I've read several explanations of how it is but none that explicity give the reason why it is so. I found the following online at grammar.about.com:
Is there a conceptual basis to the grammatical distinction between count nouns and mass nouns? One answer is that this grammatical distinction is, to a very large degree, semantically opaque and unprincipled . . .. In general, people learn which nouns are typically used as count nouns and which are typically used as mass nouns without any understanding of why these differences in syntax occur. Another answer is that the grammatical distinction between count and mass nouns is to a very large degree conceptually based. That is, when speakers use count nouns to refer to things they implicitly have something in mind that they are trying to communicate that is common across all uses of count nouns. A similar view applies to the use of mass nouns. A third answer, and the one that I propose, is that the count-mass noun distinction is to a very large degree conceptually based, but there are exceptions. Some exceptions do not seem to have a clear explanation, but others may occur because of competing communicative functions of language.
Here's Wikipedia's take:
In English (and in many other languages), there is a tendency for nouns referring to liquids (water, juice), powders (sugar, sand), or substances (metal, wood) to be used in mass syntax, and for nouns referring to objects or people to be count nouns. This is not a hard-and-fast rule; however, mass nouns such as furniture and cutlery, which represent more easily quantified objects, show that the mass/count distinction should be thought of as a property of the terms themselves, rather than as a property of their referents. For example, the same set of chairs can be referred to as "seven chairs" and as "furniture"; although both chair and furniture are referring to the same thing, the former is a count noun and the latter a mass noun. The Middle English mass noun pease has become the count noun pea by morphological reanalysis.
For another illustration of the principle that the count/non-count distinction lies not in an object but rather in the expression that refers to it, consider the English words "fruit" and "vegetables". The objects that these words describe are, objectively speaking, similar (that is, they're all edible plant parts); yet the word "fruit" is (usually) non-count, whereas "vegetables" is a plural count form. One can see that the difference is in the language, not in the reality of the objects. Meanwhile, German has a general word for "vegetables" that, like English "fruit", is (usually) non-count: das Gemüse. British English has a slang word for "vegetables" that acts the same way: "veg" [rhymes with "edge"].
In languages that have a partitive case, the distinction is explicit and mandatory. For example, in Finnish, join vettä, "I drank (some) water", the word vesi, "water", is in the partitive case. The related sentence join veden, "I drank (the) water", using the accusative case instead, assumes that there was a specific countable portion of water that was completely drunk.
The work of logicians like Godehard Link and Manfred Krifka established that the mass/count distinction can be given a precise, mathematical definition in terms of quantization and cumulativity.
When we talk about shrimp or fish in the singular but the referent is multiple, we are referring to it as a material in which the individuals are not visible or important. This is the same way that we talk about paper or meat, and as there is only one material it is singular. This is often the case where the thing being referred to is useful to us in some way. Food or drink for example.
An example of this is that we talk of a castle being built of stone, because we are not interested in the the individual stones, but would talk about a wheelbarrow full of stones being taken to the castle.
It is not clear cut though. Some people will talk about a herd of elephant, others a herd of elephants, and we have a flock of sheep but a herd of cows. One explanation for this is that sheep tend to run around in one mass in which the individuals are lost (the same as fish or shrimp) while cows spread out as individuals, but that would not explain the herd of elephant.