1. toddler 
[noun]
[de peu-ter, de peu-ters]
A "peuter" is a child from 1 year old until approximately three years old, i.e. the age that the child goes to kindergarten. From that point on they're called "kleuters".
The age barrier between "peuter" and "kleuter" is not very distinct, though. "Toddler" can be used as a translation for both "peuter" and "kleuter". Fact is that a "peuter" is younger than a "kleuter".
Examples:
– "Kleine Luke is een heel leuke peuter!"
("Little Luke is a very sweet toddler!" Lit.: "…a very nice toddler.")
– "Sara is een erg drukke peuter, dat belooft wat voor de pubertijd…"
("Sara is a very active toddler, puberty will be a blast…" Lit.: "…that sounds promising for puberty.")
Related words:
– Baby: baby [noun] [de baby, de baby's].
– Kinderopvang: children day care (center) [noun] [de kinderopvang, <no plural>].
– Kleuter: little boy/girl, infant, toddler [noun] [de kleuter, de kleuters].
Example:
– "Ik heb je hulp nodig!" – "Onzin, je bent toch geen kleuter?!"
("I need your help!" – "Nonsense, you're not a little boy, are you?!")
– Zuigeling: baby (lit.: suckling) [noun] [de zuigeling, de zuigelingen].
2. to pick one's nose, to fumble, to tinker, to tamper
[verb]
[peu-te-ren, peu-ter-de, h. ge-peu-terd]
"Peuteren" generally translates to "to fumble/tinker", but when applied to one's nose, the appropriate translation is "to pick one's nose".
In case of nose picking, you can also use "neuspeuteren", but only as an infinitive. When conjugating, "peuteren" is usually combined with "in je neus" (in one's nose), see the Examples.
Examples:
– "Frank houdt erg van neuspeuteren…" – "Waardeloos…"
("Frank loves to pick his nose…" – "That sucks…")
– "Don peutert te pas en te onpas in zijn neus…" – "Een onverkwikkelijke situatie…"
("Don picks his nose all the time…" – "An unpleasant situation…")
Related words:
– Neus: nose [noun] [de neus, de neuzen].
Example:
– "Pardon, ik moet even mijn neus snuiten."
("Excuse me, I have to blow my nose.")
– Pietepeuterig: very detailed, finicky [adjective].
– Pulken: (syn. to "peuteren") to pick one's nose [verb] [pulken, pulkte, h. gepulkt].
– Snot: mucous [noun] [het snot, <no plural>].
– Snuiten: to blow one's nose [verb] [snuiten, snoot, h. gesnoten].
This is a bit of a minefield in English too.
“Fact is that a “peuter” is younger than a “kleuter”.”
Here (UK) a little one younger than a toddler would probably be an “infant”.
But, children who are older than toddlers go to a primary or infant school, people sometimes referring to them as being in the “infants” class.
I guess a child may be both an “infant” and a “toddler” at the same time.
In English, “toddler” refers to the stage when a child is learning to talk and takes uncertain steps. Random House Dictionary suggests that the origin is a portmanteau of “totter” and “waddle” dating to the late 1400s. Once a child can walk steadily, toddler is seldom applied.
While “toddler” is a reasonable translation for “peuter”, the ages involved for the word “kleuter” would make “little boy/girl” the more natural rendering for the latter.
In the US, a child of less than five years or so is called a “pre-schooler” and as mentioned, “toddler” is reserved for those children too young to walk and run steadily – I’d say up to two years old.
“Infant” derives from the French “enfant” and is used in the UK as above, mainly in the context of school. In the US, “infant” usually refers to a fairly young baby – older than a newborn, younger than a toddler.
The informal English word for mucous, “snot”, MUST be linked with snuiten!
Another wonderful related word: “pietepeuterig”. It means something like “very detailed”, “finicky”, or even “too elaborate”.
@Amy: I’ve added “snot”!
@Marco: I’ve added “snot”!