Repetitive behaviours are not unique to the autism community. Examples of repetitive behaviours include: feet tapping, cracking knuckles and listening to the same song on repeat.
Repetitive behaviours can be repetitive motions, repetition of words (echolalia), vocalizations and repetitive movement of objects. These behaviours are also known as stimming and self-stimulating behaviours. While most people can control when they exhibit repetitive behaviours, they are often involuntary for people with autism.

Repetitive behaviours vary from person to person. Each individual with autism has a unique self-stimulating behaviour. These behaviours can be consistent throughout a person’s life, but can often change over time. For example, one person may flap their hands as a child, use a fidget toy as a teenager and paint as an adult. Here are some other common repetitive behaviours for different senses;
Visual: finger flicking

Auditory: making vocal sounds

Tactile: hair twirling

Taste: licking objects

Smell: smelling objects

Vestibular: rocking front to back

Proprioception: jumping

To reduce sensory input

Many autistic people will stim to reduce the level of sensory input experienced. It is also a way to reduce the likelihood of experiencing a meltdown or shutdown.

To gain sensory input

Some individuals may seek sensory stimulation. For example, jumping on a trampoline or lifting something heavy this is a way to regulate emotional and behavioural responses to sensory stimulation.

Many self-regulatory behaviours are used to reduce stress and anxiety. Focusing your attention on stimming rather than what is causing anxiety can be calming for many people.

Stimming is not always about avoiding a meltdown. Many people with autism will exhibit repetitive behaviours when they are excited or happy like echolalia or jumping up and down.

Yes. It is very important for people with autism to be able to use repetitive behaviours. These behaviours are a way to regulate emotions and behaviour. If these are stopped, it would cause a great deal of distress to the person.
However, there are some repetitive behaviours which may put someone with autism at risk. These include head banging, hair pulling and self-harming.
It is important to keep someone safe if exhibiting self-harming behaviours. For example, providing alternatives or increasing structure could help reduce self-harming behaviours.

Head banging could be replaced using a swing. This will provide a similar sensory experience.

A sensory bag, of carrots or chewing gum could be a safe alternative to nail and finger biting.

This may help reduce anxiety and increase the predictability of the day which may reduce self-harming behaviours.

If the behaviour is driven by anxiety, seeing a mental health professional would be beneficial.