You will encounter "ouder" in the meaning of "parent" (see 1.) or as the comparative degree of "oud" (see 2.)

1. parent

[noun]
[de ou-der, de ou-ders]

Examples:
– "Haar moeder is een alleenstaande ouder." 
("Her mother is a single parent.")

– "Beide ouders dienen bij het gesprek aanwezig te zijn." 
("Both parents are required to be present during the consult.")

– "Zij is een kind van gescheiden ouders." 
("She is a child of divorced parents.")

– "De ouders van je ouders worden ‘grootouders’ genoemd." 
("The parents of your parents are called ‘grand parents’.")

Expressions:
– "Aanstaande ouders": expectant parents.

Example:
– "De aanstaande ouders begonnen al aardig zenuwachtig te worden."
("The expectant parents were starting to get pretty nervous." Note the use of "aardig": it can mean both "nice/friendly" or "quite/pretty".)

Related words:
– Kind: child [noun] [het kind, de kinderen].
– Ouderschap: parenthood [noun] [het ouderschap, <no plural>].

Example:
– "Ik neem al mijn ouderschapsverlof op"
("I’m taking all my parental leave." Note that maternity leave is something different: "zwangerschapsverlof".)

2. older
[comparative degree of "oud"]
[ou-der]

"Ouder" is also the comparative degree of the adjective "oud": old. A related noun derived from "ouder" is "oudere", but you will in fact only encounter it in its plural form "ouderen": elderly people.

Examples:
– "Ik ben ouder dan mijn zusje, maar ik ben niet de oudste." 
("I’m older than my (baby) sister, but I am not the oldest.")

– "Ik had mijn nicht al een tijd niet meer gezien; zij ziet er nu echt een stuk ouder uit!" 
("I hadn’t seen my cousin for quite some time; she really looks a lot older now!" Note that there a different words in Dutch for male or female cousins: "neef" and "nicht". A common mistake Dutch people make is to talk about their nephew or niece instead; this is because these are also called "neef" and "nicht" in Dutch. And while I am on the topic, note that "nicht" is also slang for a homosexual.)

Related words:
– Ouderdom: old age [noun] [de ouderdom, <no plural>].
– Ouderen: elderly people [noun, plural] [de ouderen].

Example:
– "Georganiseerde busreizen zijn populair bij ouderen."
("Organized bus tours are popular with elderly people / senior citizens.")