Actions as Nouns
In Russian, present active participles—words ending in -щий describing "the one who is doing [action]"—frequently act as standalone nouns. We call these "substantivized participles."
For instance, отдыхающий literally means "the resting [person]," but is used as the noun for "vacationer." Similarly, управляющий means "the managing [person]," or "manager."
Declining Like Adjectives
Even though these words act as nouns, they still take standard adjective case endings. For example, a masculine participle ending in -ий changes to -его in the Genitive or Accusative case, and -ему in the Dative case.
Describing Categories of People
This pattern is very common for categorizing people based on what they do. You will often see these words in the plural to refer to groups, such as smokers (курящие), public speakers (выступающие), or interested volunteers (желающие).
Reflexive Participles
If the base verb is reflexive (ending in -ся or -сь), the participle keeps that particle attached to the very end.
A common example is учащийся (learner), from учиться (to study). When declining, the adjective ending changes before the -ся. Notice how the plural form учащиеся combines the adjective ending -ие with the reflexive -ся.
Travel and Work Terminology
You will frequently hear these terms at train stations and airports. Announcements routinely address greeters (встречающие) and those seeing people off (провожающие).
In professional contexts, an inspector is often referred to as "the checking one" (проверяющий).