A second charge is typically a secured loan taken out by the home owner, or it could be charge put on by a creditor following a court order in respect of a debt. Either way, its pretty appalling that the vendor didn't mention it to his solicitor, and worse that the vendor's solicitor didn't spot it.
The searches are done by YOUR solicitor. He would have spotted the 2 charges on the register but wouldn't necessarily have thought anything of it as he would not know the total amount outstanding.
However, I don't understand why it is causing an issue. All it means is that the vendor's solicitor, when he receives the money from you, doles out a wodge to the mortgage company (the 1st charge) then doles out a second wodge to clear the 2nd charge debt. What's left goes to the vendor. The only way its a problem is if the sum of the two charges is greater than the price you are paying.
Get onto your solicitor and ask him to find out why it is a problem (or phone your vendor yourself).