A tubular neighborhood of a smooth embedded submanifold is a neighborhood identified with a neighborhood of the zero section in its normal bundle. Radial deformation of punctured fibers gives the sphere bundle, and excision identifies the associated pair with a normal disk-bundle pair.
A smooth embedded submanifold has a neighborhood diffeomorphic to a neighborhood of the zero section of its normal bundle, with the zero section identified with the submanifold. One may prescribe the normal-bundle splitting of the derivative along that section. Choose a Riemannian metric making the splitting orthogonal and use its normal exponential map: its derivative there is the required isomorphism, so the inverse function theorem supplies local diffeomorphisms. A sufficiently small, possibly varying, fibre radius makes these fit into a tubular neighborhood.
A compact smooth embedding has a tubular neighborhood identified with its normal bundle. Collapse the complement of its open disk neighborhood to the basepoint and identify the remaining quotient with the Thom space of that normal bundle. Pulling back its Thom class constructs a Gysin class. For a graph embedding into a product with Euclidean space, desuspending the auxiliary coordinates gives the corresponding wrong-way map.
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A tubular neighborhood is a concept from differential topology, which refers to a certain kind of neighborhood around a submanifold within a manifold.