In relation to babies, the term weaning can have various meanings. It all depends on the context you use it in.
Another method of weaning is stopping cold-turkey, which can be very upsetting to a child, thus the "Don't offer, don't refuse" method is very popular.
Usually, weaning refers to the process of getting a baby off of breastmilk / formula and onto solid foods. This process is gradual and starts from 6 months of age when the baby's gut has matured. You start to introduce solid foods and increase the quantities over a period of time.
As your child starts to eat more and more solid foods, she will drink less breastmilk / formula over time and eventually leave breastmilk / formula completely (After a year at the earliest). Then your child has been weaned.
It is important to remember that as you introduce solid foods, breastmilk / formula remains your baby's main source of nutrition for the first year of life. Therefore you always offer breastmilk / formula first at meal time before offering the solid foods.
You also often hear the term "self-weaning" among breastfeeding mothers. As breastmilk remains beneficial to your baby irregardless of age, some mothers choose to breastfeed their babies until they "self-wean", often when they are toddlers. They thus leave the decision up to the baby to determine when nursing stops and they let nature take its course. (Not to be mistaken for a nursing-strike in babies under the age of a year, as babies under one do not self-wean)
Another method of weaning is stopping cold-turkey, which can be very upsetting to a child, thus the "Don't offer, don't refuse" method is very popular. With this method the mother does not offer the breast, but also never refuse a request from the child.
With the process of introducing solids into a baby's diet, there is also two methods to choose from; Traditional Weaning and Baby Led Weaning.
Traditional Weaning refers to the method of spoon feeding your baby puree's on a date determined by the parent, deciding the baby is ready.
Whereas the new method of Baby Led Weaning takes its cues from the baby, the baby's development and body. Food is offered in its natural form and the baby goes through the natural process of learning to eat with first being able to pick up the food, bringing it to her mouth, taking a bite, chewing and swallowing. Allowing the baby to indicate when they are ready to eat.