Y is a pronoun.

In your case, y replaces a noun or a noun group introduced by à or its derived forms (aux, au), because the verb affecter (to appoint or to assign, in this context) is used with the à in French.

Affectez 10 citoyens à cette tâche pour produire des matériaux de construction.

The exception to this rule is when the noun is a person.

J’écris à ma mère. → Je lui écris.

Je pense à mon père/ma mère. → Je pense à lui/à elle.

Y should be placed before the verb, but in your example there is an inversion because of the use of the "impératif". Y is therefore placed after the verb with a hyphen for the link.

Note: y is also used to replace a location (introduced by chez, dans, sur, à…), but this is not your case.

-y is used to avoid repetition by referring to a previously mentioned entity.

Construisez une usine.

Affectez-y 10 citoyens pour produire des matériaux de construction.

Here -y refers to une usine mentioned in the previous sentence. So the sentence means:

Affectez à l’usine que vous avez construite 10 citoyens pour produire des matériaux de construction.

In English this would be:

Build a factory.

Assign it 10 citizens to produce building materials.

In English this it has the same usage as -y does in French.