The term is more common in British English than American, where 'stroller' is used. In the UK, you'll often hear parents refer to their stroller as a perambulator.
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Old-Fashioned Tone
Using 'perambulator' can give a quaint, old-fashioned feel to your language. The old photograph showed a woman with a large-wheeled perambulator.
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Formal Context
'Perambulator' may sound overly formal; 'pram' or 'buggy' is more casual. For a walk in the park, simply take the pram instead of saying 'perambulator.'