.a are static libraries. If you use code stored inside them, it's taken from them and embedded into your own binary. In Visual Studio, these would be .lib files.
.so are dynamic libraries. If you use code stored inside them, it's not taken and embedded into your own binary. Instead it's just referenced, so the binary will depend on them and the code from the so file is added/loaded at runtime. In Visual Studio/Windows these would be .dll files (with small .lib files containing linking information).