I think the idea is that, in the partnership that preceded Berkshire Hathaway, shareholders had a right to sell their shares (partnership interests) back to the partnership. This right created a drain on the partnership capital because the partnership would have to take money “out of the till” — literally, out of the cash register, but here figuratively meaning out of funds that would otherwise be available for investment. But at Berkshire Hathaway, shareholders can sell their shares to other members of the public but cannot sell the shares back to the company. So, the company does not face the risk that it will unexpectedly have to pay out capital to shareholders. Consequently, the company has more control over its capital for investment purposes.

A "till" is the drawer in which a cashier keeps money. A bank "teller" works at a "till," (the "i" somehow changed to an "e"). Here, "till" is being used figuratively to mean some kind of cash reserve that his corporation holds in cash. It is inconvenient or worse to have to pay out cash when you would rather use it to finance business expansions. Buffett's previous partnership had rules which allowed shareholders to redeem their shares directly with the partnership and receive cash from the partnership, whenever they wanted. Each redemption drains cash from the partnership's capital. Now he runs a corporation which issues stock. Companies are not required to redeem shares. Stockholders don't mind this because they believe they can sell their shares to a willing buyer in the market. Suppose I hold one share of BRK.B stock. I want to "liquidate" it, I don't want the stock any more, I want money. Can I go to Berkshire Hathaway and say "Here's my stock, I want my money?" No, I can't. But I can easily find a buyer in the stock market who is willing to buy it from me and pay me $219. I can liquidate my share of stock by myself, without Berkshire Hathaway knowing or caring about it.

I'm not a business major, but I think the statement means that payments could be made from 'cash on hand' from daily operations as the company probably has a lot of cash that has not been committed to purchases yet.