OK, now it makes sense!

Here's the thing, you are currently producing +152 Tourism per turn (as you can see at the top of the screen, next to your culture and faith, and in the Overview, where it says "Current Tourism Output:").
In regard to Venice, you reach Influential with them (so you have more lifetime tourism against them than they have lifetime culture), and have a +50% modifier in tourism against them (so you probably have a Trade Route to them and Open Borders or something like that). This means that, per turn, you are producing +228 Tourism against Venice.
However, you are also told the trend is Falling. This means that Venice increased the amount of culture they make per turn, and are now making more than +228 Culture per turn - hence your influence falling.
To turn the situation around, get more tourism by creating Great Works or by completing theming bonus in your museums and Wonders. Try to propose and be the top contributor in the International Games Project to gain a boost in Tourism for a number of turns. You can also build Hotels, Airports, the National Visitor Center, and research The Internet - all of which increase your Tourism output!
Hope that was helpful!