The days between Shiva Aser B'tamuz and Tisha B'av are referred to as "Ben Hametzarim" (the dire straits) based on the verse in Eichah (1:3).
Shibbolei Haleket (263) references the verse in Daniel (10:2), which says, "Daniel mourned for three weeks," as referring to the three weeks of Ben Hametzarim.
During this time, we are in a state of mourning with halachos comparable to mourning the love of a loved one. We find this in the Gemara Taanis (30a) which teaches that anything that's prohibited for a mourner during aveilus is forbidden on Tisha B'av.
The Gemara in Yevamos (43b) tells us that even the week before Tisha B'av is considered a time of aveilus, albeit on a lower level than regular aveilus.
According to the Ashkenazi custom based on the Rema (551:2) and even earlier by the Meiri in Taanis (30b), some forms of mourning begin from Shiva Aser B'tamuz.
Then, on Rosh Chodesh Av, we start a higher level of mourning as the Shulchan Aruch outlines (551:1-2).
It gets more severe on Erev Tisha B'av (553:2) and even more intense on Tisha B'av itself (554:1-25).
All this differs from mourning a deceased relative, which follows the reverse order. It begins with the most intense until the body is buried, followed by Shiva, for a week. Then comes the lower level of Shloshim, which will last a month. Finally, the aveilus ends after twelve months. So, although Ben Hametzarim mirrors aveilus, it follows the reverse order.
