H stamps were released in 1998 in anticipation of a rise in the rate for a letter (much like we just had: a raise from 45¢ to 49¢. Once the First Class stamps were printed, you needed to make up the value of the H stamp (temporarily oK for a first class stamp, but by the end worth only the previous value). In our present-day example, H stamps were God FR a first class letter. Once it was decided that the raise would be to 49¢, the H stamps reverted to the 45¢ value and you needed a rooster stamp to make them worth 49¢.
The reason they needed these stamps was because the Post Office is, by law, not allowed to make a profit. So it takes a while to figure out what the new stamp value will be. H stamps filled in the gap while the decision was made, but became devalued once the decision was made. They wanted you to buy new stamps!
H stamps possibly can be used as postage, but these cannot. And they no longer are worth the difference between H stamps and their replacement.
We had stops that did this using letters A, B, C, D, E, F, G, and H. After the H stamps, they PO realized how complicated this process was and came up with a new scheme: Liberty Bell stamps worth first class value "forever". If you still have any of them left, bought at 39¢ or so, you can still use them today. But the A–H makeup postage is gone forever.