This essentially means that the shareholders of the target company have agreed to sell to the bidder.
There may be some shareholders who still refuse to sell. The level at which a bid becomes unconditional as to acceptances is usually set high enough to allow them to be compelled to sell (a compulsory acquisition).
The bidder may choose to declare the bid unconditional as to acceptances before the original required level of acceptances has been reached. Even in this case, an offer may not become unconditional before acceptances are sufficient (together with the bidder's existing stake) to give the bidder a 50% stake in the target.
Even after an offer has become unconditional as to acceptances, there may remain other conditions that have to be met. The commonest examples of these are approval from competition regulators and approval from the bidder's shareholders.
Once all conditions are met, the offer becomes "unconditional in all respects" and the takeover is certain to go ahead. The City Code sets deadlines by which the offer must be declared unconditional as to acceptances and unconditional in all respects.