During the election the FBI (Federal Bureau of Investigation) was recording some conversations that involved people of interest in FBI investigations and members of Donald Trump's campaign. We don't have complete information on this. Trump did not clarify what he meant. Some possibilities:
CNN said that there was an active warrant during and after the election on Paul Manafort. This included recording some of his phone calls. We do not know if any of those phone calls involved Trump or members of the campaign other than Manafort.
Former FBI informant Carter Page was also subject to surveillance, including the recording of phone calls. Page was trying to get a job as a foreign policy advisor with the Trump campaign, possibly seeking a job in the Trump administration. It is unclear if any recorded phone calls involved Trump or other members of the campaign.
The Daily Beast notes that Michael Flynn was recorded on multiple phone calls with foreigners who were under surveillance. It is unclear if additional surveillance was done directly on Flynn. The nature of the original surveillance was such that the identities of any US citizens should have been left out of the transcripts until a warrant was obtained. If any additional surveillance was done on Flynn, we do not know if any phone calls involved Trump or other members of the campaign.
While we don't know if these calls involve Trump or the campaign, it is entirely possible that Trump knew.
Some people seem to be making a distinction between illicit wiretapping performed by illegally adding an electronic device to the phone and legally-sanctioned surveillance with the assistance of the phone company. There is no evidence of the former. However, it is not true to say that evidence of the latter would be meaningless. It is entirely possible for a government to abuse its legal powers of surveillance for partisan purposes.
Trump doesn't seem to particularly care about such fine distinctions. His public statements suggest it was wrong for his political opponents to get information from phone calls that he and his staff were making during the campaign. He doesn't seem to care about how that information was obtained.
Of great suspicion is the ongoing attempt to deny that anything happened.
There was no wiretapping. OK, for some definition of wiretapping, that's true. But for a broader definition, it isn't. If "wiretapping" means any way of obtaining the audio of a phone conversation, then they certainly obtained such audio.
Any surveillance was legal. Possibly true. It is also perfectly legal to convict an innocent person of wrongdoing. That doesn't make it right. We have systems to try to avoid this and to fix it when it happens.
If Trump and his campaign had not been speaking to these people, then they wouldn't have been surveilled. Possibly true. But a counter to this is what information about similar conversations involving the Hillary Clinton campaign was supplied to partisans opposed to her? That has not been explored.
Why wasn't Trump informed during the campaign of the issues with Manafort, Page, and George Papadopoulos?
It seems like it should be possible to find people in the FBI who would not leak to partisans (particularly including political appointees) and still would have investigated any allegations thoroughly. Why weren't such people put on these investigations and partisans like Peter Strzok moved to other things? Or at least separated from the raw information until after the election?
If there was nothing to this story, then why the ever shifting excuses? Why not just simply say in the beginning that there was perfectly normal surveillance occurring? They could then explain how they avoid the problematic things. For example, what kept information from the surveillance that involved campaign secrets from leaking to partisans in the administration and thence to Clinton's campaign?
Of course, since such information was leaking, perhaps the problem is that any system they had in place was either inadequate or not enforced. And that's the real scandal. That supposedly confidential information from ongoing FBI investigations was going to political partisans who were then sharing it with people opposed to those being investigated. That seems wrong.