Allotment is the allocation of securities to applicants for a new issue.
The allotment process is trivially simple if an issue is not oversubscribed: each applicant gets whatever they applied for. If an issue is oversubscribed (as happens with popular IPOs) then some mechanism has to be used to decide how many shares each applicant gets.
Pro-rata allocation is a very common method of allocation. Every applicant gets the same proportion of what they applied for. Some applicants can be left with so few shares that they would probably prefer not to have applied. Another problem is that applicants can be tempted to apply for more than they really want, in order to get the amount they actually want.
Auction processes are sometimes used and the shares (or other securities) go to the highest bidders. Everyone pays the same price, not the price that they individually bid. The price is set at exactly the level that allows the issue to be fully subscribed.