Filling any type of hollow masonry block with concrete makes it stronger as soon as the concrete dries. Rather than all the stress being on the outer walls of the block, pressure is spread throughout the solid block. This is useful if you're building a foundation for a building or installing a walkway and don't want hollow spaces.
Strengthening hollow blocks with concrete by making them more dense and eliminating empty space in block walls also enhances thermal insulation. This is useful primarily in basement construction. Concrete, along with foam-based insulation materials, can help block walls keep heat in the home during the winter. This is especially important for homeowners with basement living space; much of the basement's heat rises to upper stories, making it difficult to keep the basement warm.
Just as filling masonry blocks with concrete makes them stronger, it also increases their weight. This can be a liability when you want a lightweight construction material, but it's an advantage in other cases. Heavier blocks compact loose soil to form garden walls and outdoor walkways that are even and flat. Heavy filled blocks are also more useful in applications where they need to remain in one place, such as stairs or doorstops.
When you pour concrete into blocks to strengthen them, you are also adding material that is very dense and therefore does a poor job of transmitting sound. Filling an outdoor block wall with concrete helps provide sound privacy as well as visual privacy. A basement wall filled with concrete keeps the home quieter -- which can be especially good if there is an underground structure such as a subway nearby.