Apportionment of local [or special] assessment

What does Apportionment of local [or special] assessment mean in American Law?

The definition of Apportionment of local [or special] assessment in the law of the United States, as defined by the lexicographer Arthur Leff in his legal dictionary is:

The apportionment of the burden of taxation arising out of a local or special assessment made to pay for locally beneficial governmental improvements, e.g., sidewalks or sewers. Various formulae are possible, e.g., linear feet of benefited property abutting the sidewalks, value of abutting houses, etc. Almost any rational, i.e., not arbitrary or discriminatory, formula will be upheld.