They were supporting Russia economically by purchasing energy (gas mainly) from them. They basically had the crazy idea that economically intertwining themselves with Russia and making themselves dependent on Russia would magically turn Russia into a modern, democratic European nation, basically "if we bring them into our club, they'll come around to our way of thinking". It didn't work, just like economically integrating with China hasn't turned China into a western-like nation either, it's only enabled the authoritarians.