The vertices of a mesh are defined around a center point of the mesh. To convert vertices to world space, they are multiplied by a matrix called model matrix.
Since we’re looking at the scene from a camera, we need to convert the vertices from world space to camera space. This is done by multiplying the vertices by a matrix called view matrix.
Once we know the vertices in camera space, we need to project them onto the screen. For that, we multiply the vertices by the projection matrix.
Instead of multiplying the vertices with 3 different matrices, we can also first multiply the 3 matrices with each other and then multiply the vertices with the resulting matrix. This resulting matrix is called modelviewprojection matrix or mvp. Of the other two you mentioned: modelview is the product of model and view matrix and projection is just the projection matrix.
All this is basic 3D graphics and is described thoroughly in most computer graphics books.