As with the athletes at the focus of this earlier question on Sports Stack Exchange,
the national association is banned from involvement. This means no organisational presence, no Russian flag, no Russian anthem;
some individuals have specific bans, including a variety of athletes, coaches and training staff, and senior administrators (some for covering up doping, but a small number for possible doping in their time as athletes);
individual athletes may (apply for and receive dispensation to) compete on their own, by proving they are not involved in any doping.
This contemporary BBC article describes the decision similarly and quotes relevant person's outlining:
But athletes who can prove they are untainted by the doping scandal will be able to compete under a neutral flag.
However, Travis Tygart, chief executive of the US Anti-Doping Agency, said not imposing a blanket ban on all participation by Russian athletes - even under a neutral flag - is a "devastating blow" to clean athletes.
Triple Olympic medallist Kelly Sotherton, who was retrospectively awarded her 2008 heptathlon bronze after Russia's Tatyana Chernova failed to have a doping ban overturned, says she understands why tougher sanctions were not imposed.
"I think they are thinking of the majority of athletes who are doing the right thing, not the wrong thing," she said.