First let's not look at it as a ♯V chord, but a ♭VI chord. This chord naturally occurs in the parallel minor and can easily be borrowed.
Let's look at how the notes move with a sample progression in the key of C:
IV F - A - C
♭VI(7) A♭ - C - E♭ - (G)
I C - E - G
If you look at this progression without the 7th, you'll notice a few different different features it has. First and most noticeable C (the tonic) is a common tone in each chord. You can think of this as linking all the chords in the progression. Next the progression descends chromatically from A (the submediant) to G (the dominant). In general chromatic movement across multiple chords is typically extremely effective especially when dealing with chords outside the key. Last the 3rd of the tonic is approached in a circular fashion going from F to E♭ to E. It's not quite a resolution, but in the context of the progression it can be viewed as a a resolution similar to the Neapolitan chord to dominant to tonic functions.
With the seventh included in the progression all that really changes is there is another common tone between the ♭VI and the I as G is common in both.
One of my favorite progressions is I - ♭VI - IV - V which is follows similar logic as mentioned above just with the added V chord to round it back to I. I personally really like using the ♭VI chord because in my opinion it sounds slightly darker in nature, maybe because it uses the ♭3 of the key or because it is from a minor key, and in my option gives the progression a slightly darker sound.