Neither 'house' nor 'shed' nor 'and' refer to any physical things. Your house (that is, the referent of the expression "my house" as uttered by you; if you have a unique house) is a physical thing, which may have a shed in it, which is also a physical thing. But the expression/term 'house' refers to an abstract entity, which we take to be the plurality/class/set of all houses. Similarly for 'shed', 'dog', and so on. A particular house, a particular shed, a particular dog, may be referred to by 'house', 'shed', and 'dog', but only if the context of utterance is such that it unambiguously determines the connection between the general term and the particular individual in the domain of discourse. That much about terms.
§1 And1 : Sentence × Sentence → Sentence
The word 'and' is usually introduced as a sentential connective: a function on the sentences of some underlying language. E.g. "p and q" is taken to be the sentence r which is true just in case p and q are true. This means that 'and' can be taken to be referring, with respect to some language L, to the set consisting of all triples (P, Q, R) s.t. R is true iff P and Q both are. From the category-theoretic point of view this explication of functions is certainly problematic, but that's an issue for another occasion.
The conclusion then is that 'and', like 'house' and 'shed', both refer to sets of entities: in the case of 'house' and 'shed' we're dealing with a set of physical entities; in the case of 'and' we're dealing with a set of linguistic and thus abstract entities. I.e., those terms are similar in that they both refer to abstract entities, but different in that those abstract entities they refer to contain entities of different kinds.
§2 And2 : Term × Term → Term
It's worth noting that in some logico-mathematical settings 'and' is overloaded: 'and1' is the usual and that connects two sentences, and 'and2' is a function between not sentences but terms. For example, "a and b" is taken to be the plurality that consists of individual a and individual b. That's the logical explication of the grouping idea Mozibur mentioned. To illustrate my earlier point about 'and' referring to an object, let's look at the referent of 'and2'. It's a function from a pair of terms to another term, so set-theoretically, 'and2' refers to the set of triples (a, b, c) s.t. c is the unique term s.t. for all properties φ, we have φ(c) iff φ(a) and φ(b). For example, if a is a red rose and b is a red lobster, then 'a and b' is their 'group term' of which we can truly predicate 'is red'. That's the general, informal, idea of this second, grouping sense of 'and'. If I find any appropriate readings on that I'll append to this post later.