Sure, I'll take a swing.
Putin is a dictatorial thug whose enemies keep dropping dead of "unfortunate accidents." He is pushing towards fully re-establishing the totalitarianism of the old Soviet Union. Under the guidance of his shirtless, macho leadership, Russia is turning homosexuality into a crime, and has recently made domestic abuse LESS of a crime, prompting a huge upswing in spousal beatings. And that's really just the start, he is NOT a nice man.
So now Flynn has quit--probably to forestall charges related to espionage or national security violations--but Trump continues to flout even the most basic national security protocols. Trump dumped the White House chief information security officer earlier this month, the guy responsible for making sure presidential communications are secure, and has not replaced him. Although he has been issued the special encrypted presidential smartphone, he continues to use his old, unsecured Android phone. There are people in the Pentagon now who have already said that the White House situation room is no longer a secured space, and Russia or other governments might be listening in.
It's not that it's bad to have ties with another country. It's the rumors that Trump in particular may have received large financial compensation for favors to be-rendered in the future.
For example, 19.5% of Rosnef stock was transfered to an unknown party recently. This is worth a very large sum of money. The Russians however need Exxon expertise to exploit certain oil deposits. We have placed sanctions against Russia preventing this.
The point is a President is not supposed to view the position as a way to personally enrich himself, but to serve the greater interests of the nation as a whole.
As for other reasons some people may be concerned with Russia - Trump has called NATO useless. NATO basically exists to contain Russian expansion. Various European countries are nervous (Poland and smaller Baltic States for example). Russia claims to be helping 'oppressed Russian minority', goes in with troops. See Georgia and Ukraine recently.
The leader of a country (and its government's advisers) must have one loyalty and that is to their country.
Anything that puts that into doubt is of deep concern for the citizens of that country.
Big swing there buddy!