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I am not a cosmologist but as I understand it, "inflation" normally refers to the very rapid expansion of the universe in the very first tiny fraction of a second after the big bang.
The universe since then has been expanding and current thinking is that the expansion is actually accelerating due to the presence of dark energy. The expansion is occurring throughout the universe. One way of thinking about it is that the universe is a four dimensional spacetime entity, but we see it as a 3 dimensional universe. Take a balloon and draw dots on its surface. As you blow it up it is expanding as a 3 dimensional entity, but from the point of view of a being on it's surface viewing in 2 dimensions, all the dots are moving away from each other. And that expansion is occurring all over the surface at the same time.
The balloon is analogous to viewing a four dimensional construct in three dimension, just deducting one dimension.
Of course this expansion is at the large scale. Locally other forces are at play. For example, the Milky Way and the Andromeda Galaxy (M31) are being pushed apart by the expansion of space, BUT that force is not as strong as their mutual gravitational attraction, so they are moving closer together.
Hope this is clear enough, and as I said I am certainly not an expert. The above is simply how I think of these matters and I am happy to be corrected by any people more knowledgeable.
Malcolm
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