Why do magnets attract some objects?  Some objects can be magnetized.  If a magnet comes close, the object turns into a temporary magnet.  It is then attracted to the magnet.

Two important magnet material properties are strength and resistance to demagnetization.  A BH curve shows how these are related.

A magnet's shape affects how much self-demagnetization occurs inside a particular magnet.  This affects the external field produced by the magnet.

Simulating fields from bar magnets used for sensor applications is among the easiest electromagnetic simulation tasks.  There are two main methods for doing this:  finite-element analysis (FEA) software, and direct solutions of Maxwell's equations.

Permanent magnets can come in a variety of shapes and magnetizations.  Many sensing applications need only a simple bar magnet.  This article talks about bar magnets.

All of magnetism can be boiled down to a few simple ideas.  If you understand these, you will be in a position to understand most magnet and sensor concepts.