Ideally, these videos should talk about a real life problem which student can relate to and then showing logically how the problem can be solved. Later bringing in the right mathematical tool to solve the problem. This will have lasting impact on a student's mind. Slowly, for many of them, the question that always many possess "what is the application of maths" will be erased from their mind.
Not quite "animated", but still very nice: James Tanton Youtube
He starts with a kind of problem, sometimes applied, but often just non-standard, and then shows mathematician viewpoint on problem solution.
You may start discovering with his "Why I became mathematician" https://www.youtube.com/watch?v=b86QcxdrNF4
A guess animation and real life are opposite? On the real life side, Dan Mayer's collection of 3-Act Tasks provide many examples with video for the first act. You might need to look for the ones that are appropriate to your age group. Note: If you're not familiar with the format of '3-act tasks', you might look at Dan Mayer's TED-talk Mathclass needs a makeover
Not exactly real life, but animated and real math: I like Flatland a lot. The ed-version also comes with activity sheets, plenty of activities to this old book from Edwin Abbott can be found online. Actually there's math accessible on many grade level. from just the definition of 'dimension' to the recursive formulas counting k-dim Elements of an n-dim Cube. Very fun! There's a second part introducing the idea of different geometries using the fact, that the angle sum of a triangle is not 180° (thus - wow - we are not living on a plane but on a sphere...). But - don't want to spoil ;-).
You might already have encountered Oliver Knill's site on Math in the Movies. The site is general, but there are also animated examples appropriate for the age group you're asking for. Actually quite the opposite, but I used the episode looking at Bart Simpson solving word problems in classes, stimulating good discussions, also on 'real life situations'.
hope that's interesting to you.