Account Management at its simplest meaning is when a client is able to get a supplier or agency to handle the specific needs of the client. One way Account Management is commonly understood is when a client hires an advertising agency, and the advertising agency assigns an account executive to be the point of liaison between the agency and the client.
That account executive will then have to keep in constant communication with the client regarding the needs of the client and the account details (like what type of advertising campaign is being created by the agency for a specific product or service of the client, the scheduling of the creation of the campaign, and even scheduling of when the advertising campaign will be rolled out to be introduced to the public.)
The number of accounts one account executive may be assigned to at one time may depend on the policy of the advertising agency itself, the capacity of the account executive for work, and the complexity of each account (meaning, if the client has pretty complex business needs requiring a huge investment into a major advertising campaign, it is most likely the account executive will be required to devote himself full-time to that account alone.) If the accounts coming in are relatively minor, one account executive might be assigned several minor accounts to handle at one time.
Thus, Account Management training may refer to the specialized training an advertising agency employee undergoes to be fit for the role of an account executive. Some employers may opt not to limit themselves to just people who have academic training or a background in advertising, and may have in-house training programs geared for their employees instead.