Weighting is used to make sure samples reproduce the underlying characteristics of the population they are drawn from. For instance, in the UK 51.6% of voters are women, of these 22.5% are above 65 years of age, 23.1% have a higher education and so on. The people selected to make part of a sample may be recruited to ensure they match these proportions.
Within the context of weighting there are two major sampling procedures: Quota and stratified sampling. The relevant difference between them is the latter uses some sort of randomization device while with the former the interviewer decides whether or not to interview a person with certain characteristics. YouGov presumably applied Quota Sampling for the Brexit survey, and the gender, age and education weights they applied are shown in the following image.
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