The most likely way to look at this is that it's a movement along the demand curve. You have the theater trying to attract people to come at a different time by lowering their prices. This moves down the demand curve so that there are more people who will be willing to come at this less popular time.
There's definitely not a shift in the curve, but you could argue that weekend movies are a different product than weekday movies and that they each have separate demand curves (because some people who would go to a movie for $10 on a weekend can't go for that price on the weekday because they have to work).
So, if your choices are a shift or a move along the curve, pick the move along the curve. However, you could also argue that there are two different curves.
I must disagree with the second answer. A shift in the demand curve reflects a situation where consumers are willing to pay a larger amount (or buy more at the same amount) FOR THE SAME PRODUCT. But in this case the two kinds of movies are not the same product.
A shift in the curve would be if customers would all of a sudden pay less for a weekday movie than they would previously. In this case, they are NOT paying less for the weekday movie. They are paying less for a weekday movie than for a weekend movie and those are two different products.
As the second answer points out, the demand curve for weekday movies is different than the one for weekend movies, but it's because they're different products, NOT because there has been a shift in the demand curve.
I am not clear about the the statement of the statement in the answer above that the movies on weekdays and weekends are not the same product. However, if we assume that these are separate products, then there is no question of either movement along the demand curve or shift in demand curve itself. These concepts apply in economics only when a single product is considered.
The situation described in the question is an example of shift in demand curve.
A demand curve is a graph of quantity of a good demanded by consumers at different prices, assuming all others things being constant. When under such static condition, the supplier change the prices they ask for the good they sell, the quantity demanded by the consumers at various price is represented by the demand curve, and change in demand due to change in price is the movement of demand along a (the same) demand curve.
In contrast, when other market conditions assumed to be constant for a demand curve change, the price for the goods demanded it self changes. The example in the question represents such a situation. Generally, there are more people wanting to see movies in theaters on weekends as compared to weekdays. Because people find it more convenient and enjoyable to watch movies in theatre on weekdays, they are also willing to pay higher prices for eat. Thus the demand curve for price of admission to movie theaters on week days will be different. At each price level the demand on weekend will be higher than that on weekdays. Thus the while demand curve for weekends will shift to right as compared to demand curve for weekdays.