Apart from flat shading (instead of smoothing, as pointed out by @atek) your mesh has a few other issues: apart some ngons, which are considered bad topology, but it could work for your needs, there are a few nonplanar faces (mostly ngons), and those are causing artifacts, as visible below.
The good news is that you can find solutions to them all using the bundled 3d print addon (you just need to activate it in user preferences), as shown below:
First, I forgot to say that before using the 3d print toolbox "check all" tool, I already recalculated normals (Ctrl+N).
- What you should have done is: try to not use ngons (ie: faces with more than 4 vertices) and if possible also avoid triangles. Why? Because this easily create problems, gives artifacts in 3d viewport and rendering, and behaves horribly if you need to animate deforming objects. The additional lines that have appeared in the render are the ngons being split into triangles as ngons themselves are not renderable.
It doesn't seem to be the case with this model but, since you're learning, it would immensely help you if you try to model everything with "quads" or, if really needed, "tris". Note that even "quads" could be made (by mistake) non planar, but while it is less likely, they will be much more easy to fix.
- What can you do now, to improve this model? This is a difficult answer. In a few words, you need to convert those "ngons" into "quads". This goes under the name of "retolopogy", ie: create a new (better, simpler) mesh structure for a shape that already exists.
I'm not a retopology genius, and without reference images it's even harder, but I tried to "fix" a small portion of the mask, by deleting faces (only faces) and subdividing remaining edges to make them nearly match their "quad" counterparts, sometimes "sliding" vertices along an edge, and rebuilding faces based only on 4 vertices.
Now, shown below, you see that after pressing "check all" again it doesn't identify those areas as issues anymore: